Have a query? Ask a Tutor!!

Access to best educators and exclusive paper discussions

Can’t find what you’re looking for?

Our tutors are from top schools around the world, and they are waiting for you 24/7, anytime, anywhere.

Homework- One to One Solutions
Understand concepts to solve better
Get your doubts solved instantly

Maths-

General

Easy

Question

Solve the radical equation $x equals square root of 7 x plus 8 end root$ . Identify any extraneous solutions

hint Hint:

Rearrange the equation and then solve for x.

The correct answer is: x = -1

Complete step by step solution:
Here given equation is $x equals square root of 7 x plus 8 end root$
On squaring both the sides, we have $x squared equals 7 x plus 8$
$not stretchy rightwards double arrow x squared minus 7 x minus 8 equals 0$
Now, this is a quadratic equation with a = 1, b = -7, c = -8
Roots can be found with, $x equals fraction numerator negative b plus-or-minus square root of b squared minus 4 a c end root over denominator 2 a end fraction$
$x equals fraction numerator 7 plus-or-minus square root of 49 minus 4 cross times 1 cross times negative 8 end root over denominator 2 cross times 1 end fraction$
$x equals fraction numerator 7 plus-or-minus square root of 49 plus 32 end root over denominator 2 end fraction$
$not stretchy rightwards double arrow x equals fraction numerator 7 plus-or-minus square root of 81 over denominator 2 end fraction$
$not stretchy rightwards double arrow x equals fraction numerator 7 plus-or-minus 9 over denominator 2 end fraction$
$not stretchy rightwards double arrow x equals 8 text or end text minus 1$

Here, on substituting x = 8 or -1 in given equation we get
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell 8 equals square root of 7 cross times 8 plus 8 end root end cell row cell not stretchy rightwards double arrow 8 equals square root of 64 equals 8 end cell end table$
Hence x = 8 works.
Now, $negative 1 equals square root of 7 cross times negative 1 plus 8 end root$
$not stretchy rightwards double arrow negative 1 not equal to square root of 1 equals 1$
Here the extraneous solution is x = -1

Related Questions to study

Does a linear , quadratic , or exponential function best model the data ? Explain.

Does a linear , quadratic , or exponential function best model the data ? Explain.

Solve the radical equation $square root of 4 x plus 5 end root minus square root of x plus 1 end root equals 1$ Check for extraneous solutions

Solve the radical equation $square root of 4 x plus 5 end root minus square root of x plus 1 end root equals 1$ Check for extraneous solutions

Solve the radical equation $square root of 3 x minus 2 end root equals x minus 4$

Solve the radical equation $square root of 3 x minus 2 end root equals x minus 4$

parallel

Does a linear , quadratic , or exponential function best model the data ? Explain.

Does a linear , quadratic , or exponential function best model the data ? Explain.

The speed, v, of a vehicle in relation to its stopping distance, d, is represented by the equation v =3.57√d. What is the equation for stopping distance in terms of the vehicle’s speed?

The speed, v, of a vehicle in relation to its stopping distance, d, is represented by the equation v =3.57√d. What is the equation for stopping distance in terms of the vehicle’s speed?

Solve $open parentheses x squared plus 4 x plus 5 close parentheses to the power of 3 over 2 end exponent plus 1 equals 0$

Solve $open parentheses x squared plus 4 x plus 5 close parentheses to the power of 3 over 2 end exponent plus 1 equals 0$

parallel

The suspension cables from the Golden gate bridge’s towers are farther above the roadway near the towers and closer to the roadway near the middle of the bridge. You can figure out your distance from middle of the bridge, x, in feet, and height of the suspension cable, y, in feet, at your position by using the equation x = $fraction numerator square root of y to the power of negative 220 end exponent end root over denominator 0.010583 end fraction$ About how far is the cable from roadway when you are 200 ft from middle of the bridge

The suspension cables from the Golden gate bridge’s towers are farther above the roadway near the towers and closer to the roadway near the middle of the bridge. You can figure out your distance from middle of the bridge, x, in feet, and height of the suspension cable, y, in feet, at your position by using the equation x = $fraction numerator square root of y to the power of negative 220 end exponent end root over denominator 0.010583 end fraction$ About how far is the cable from roadway when you are 200 ft from middle of the bridge