Maths-
General
Easy

Question

Solve the radical equationsquare root of 6 x minus 20 end root minus x equals negative 6. Check for extraneous solutions

hintHint:

Rearrange the equation and then solve for x.

The correct answer is: x = 4


    Complete step by step solution:
    Here we have the equation square root of 6 x minus 20 end root minus x equals negative 6
    On rearranging, we have square root of 6 x minus 20 end root equals x minus 6
    On squaring, we have 6 x minus 20 equals left parenthesis x minus 6 right parenthesis squared

    not stretchy rightwards double arrow 6 x minus 20 equals x squared minus 12 x plus 36
    not stretchy rightwards double arrow x squared minus 12 x minus 6 x plus 36 plus 20 equals 0
    not stretchy rightwards double arrow x squared minus 18 x plus 56 equals 0
    Now, this is a quadratic equation with a = 1, b = -18, c = 56
    Roots can be found with, x equals fraction numerator negative b plus-or-minus square root of b squared minus 4 a c end root over denominator 2 a end fraction
    x equals fraction numerator 18 plus-or-minus square root of 324 minus 4 cross times 1 cross times 56 end root over denominator 2 cross times 1 end fraction
    On solving, we get x = 14, 4
    On substituting the value of x in the equation, we get
    square root of 6 cross times 14 minus 20 end root minus 14 equals square root of 64 minus 14 equals 8 minus 14 equals negative 6
    Hence x = 14 works.
    Now, we have square root of 6 cross times 4 minus 20 end root minus 4 equals square root of 4 minus 4 equals 2 minus 4 equals negative 2 not equal to negative 6
    Hence x = 4 does not work.
    Hence x = 4 is an extraneous solution.

    Related Questions to study

    General
    Maths-

    Use the functions shown :
    a. Evaluate each function for x=6 , x=8 and x=12
    b. When will function h exceed function f and function g ?

    Use the functions shown :
    a. Evaluate each function for x=6 , x=8 and x=12
    b. When will function h exceed function f and function g ?

    Maths-General
    General
    Maths-

    The graph shows population models for three cities , based on data over a five year period. If the populations continue to increase in the same ways , when will the population of city C exceed the populations of the other two cities ?

    The graph shows population models for three cities , based on data over a five year period. If the populations continue to increase in the same ways , when will the population of city C exceed the populations of the other two cities ?

    Maths-General
    General
    Maths-

    Calculate the second difference for data in the table. Use a graphing calculator to find the quadratic regression for each data set. Make a conjecture about the relationship between the a values in the quadratic models and the second difference of the data.

    Calculate the second difference for data in the table. Use a graphing calculator to find the quadratic regression for each data set. Make a conjecture about the relationship between the a values in the quadratic models and the second difference of the data.

    Maths-General
    parallel
    General
    Maths-

    Carmen is considering two plans to pay off a $10,000 loan . The table show the amount remaining on the loan after x years . Which plan should carmen use to pay off the loan as soon as possible ? Justify your answer using a function model ?

    Carmen is considering two plans to pay off a $10,000 loan . The table show the amount remaining on the loan after x years . Which plan should carmen use to pay off the loan as soon as possible ? Justify your answer using a function model ?

    Maths-General
    General
    Maths-

    Solve the radical equation square root of x plus 4 end root minus square root of 3 x end root equals negative 2. Check for extraneous solutions

    Solve the radical equation square root of x plus 4 end root minus square root of 3 x end root equals negative 2. Check for extraneous solutions

    Maths-General
    General
    Maths-

    Solve the radical equation square root of 5 x plus 1 end root plus 1 equals x. Check for extraneous solutions

    Solve the radical equation square root of 5 x plus 1 end root plus 1 equals x. Check for extraneous solutions

    Maths-General
    parallel
    General
    Maths-

    Solve the radical equation square root of 2 x end root equals 12. Check for extraneous solutions

    Solve the radical equation square root of 2 x end root equals 12. Check for extraneous solutions

    Maths-General
    General
    Maths-

    Solve the radical equation square root of 25 plus x end root plus 5 equals 9 Check for extraneous solutions

    Solve the radical equation square root of 25 plus x end root plus 5 equals 9 Check for extraneous solutions

    Maths-General
    General
    Maths-

    Solve the radical equation square root of x plus 9 end root minus square root of 2 x end root equals 3

    Solve the radical equation square root of x plus 9 end root minus square root of 2 x end root equals 3

    Maths-General
    parallel
    General
    Maths-

    Function f represents the population , in millions , of Franklin x years from now. Function g represents the population , in millions , of Georgetown x years from now, If the pattern shown in the table continue , will franklin always have a greater population than Georgetown ? Explain.

    Function f represents the population , in millions , of Franklin x years from now. Function g represents the population , in millions , of Georgetown x years from now, If the pattern shown in the table continue , will franklin always have a greater population than Georgetown ? Explain.

    Maths-General
    General
    Maths-

    Solve the radical equation square root of 6 minus x end root equals x

    Solve the radical equation square root of 6 minus x end root equals x

    Maths-General
    General
    Maths-

    What are the solutions to the equation left parenthesis x minus 3 x minus 6 right parenthesis to the power of 3 over 2 end exponent minus 14 equals negative 6

    What are the solutions to the equation left parenthesis x minus 3 x minus 6 right parenthesis to the power of 3 over 2 end exponent minus 14 equals negative 6

    Maths-General
    parallel
    General
    Maths-

    Escape velocity is the velocity at which an object must be travelling to leave a star or planet without falling back to its surface or into orbit. Escape Velocity V depends on the gravitational constant G , the mass M, and radius r, of the star or planet .
    V equals square root of fraction numerator 2 G M over denominator r end fraction end root
    Rewrite the equation to solve for mass,
    The escape velocity of earth is 11, 200 m/s and its radius is 6,371,000 m. The gravitational constant is 6.67x 10^-11. What is the earth's mass in kilograms?

    Escape velocity is the velocity at which an object must be travelling to leave a star or planet without falling back to its surface or into orbit. Escape Velocity V depends on the gravitational constant G , the mass M, and radius r, of the star or planet .
    V equals square root of fraction numerator 2 G M over denominator r end fraction end root
    Rewrite the equation to solve for mass,
    The escape velocity of earth is 11, 200 m/s and its radius is 6,371,000 m. The gravitational constant is 6.67x 10^-11. What is the earth's mass in kilograms?

    Maths-General
    General
    Maths-

    Calculate the second difference for data in the table. Use a graphing calculator to find the quadratic regression for each data set. Make a conjecture about the relationship between the a values in the quadratic models and the second difference of the data.

    Calculate the second difference for data in the table. Use a graphing calculator to find the quadratic regression for each data set. Make a conjecture about the relationship between the a values in the quadratic models and the second difference of the data.