What is the sum of the solutions to the given equation?

The correct answer is: 16

The given equation is a quadratic equation (i.e. Highest power of a variable is 2). We will solve the given quadratic equation and find the sum of the solutions so obtained.
Step-by-step solution:-
x² - 14x + 40 = 2x + 1
x² - 14x - 2x + 40 - 1 = 0
x² - 16x +39 = 0 -------------------------- (equation i)
Comparing equation i with the general form of a quadratic equation i.e. ax2 + bx + c = 0, we get-
a = 1, b = -16, c = 39
Using factorization method (we factorize a × c i.e. 1 × 39 i.e. 39 into 2 factors such that the addition of these 2 factors gives a value that is equal to b i.e. -16)-
∴ we factorize 39 into -3 and -13 (because -3 × -13 = 39 and -3 + (- 13) = -16)
x² - 13x - 3x +39 = 0
∴ x (x - 13) - 3 (x - 13) = 0------------- (Taking common factors)
∴ (x - 3) (x - 13) = 0
∴ either x - 3 = 0 or x - 13 = 0
∴ either x = 3 or x = 13
∴ the solutions of the given equation are 3 and 13
Sum of the solutions = 3 + 13 = 16
Final Answer:-
Option D i.e. 16 is the correct Option.
Note:-
Alternatively, formula method to solve the quadratic equation can also be used to find the solution of equation i above. Formula-