Solve for x in the equation x squared minus 14 x + 31 = 63. x = - 16 or x = 2 x = negative 7 plus-or-minus 3 StartRoot 7 EndRoot x = - 2 or x = 16 x = 7 plus-or-minus 3 StartRoot 7 EndRoot

Question:

Solve for x in the equation

x² - 14x + 31 = 63.

A. x = - 16 or x = 2

B. x = - 7 ± 3 √7

C. x = - 2 or x = 16

D. x = 7 ± 3 √7

Answer:

C. x = - 2 or x = 16

Step-by-step explanation:

Given

x² - 14x + 31 = 63.

Required

Solve for x

We start by converting the expression x² - 14x + 31 = 63. to a quadratic equation.

This is done by subtracting 63 from both sides

x² - 14x + 31 - 63 = 63 - 63

x² - 14x - 32 = 0

Expand the above expression

x² - 16x + 2x - 32 = 0

Factorize

x (x - 16) + 2 (x - 16) = 0

(x + 2) (x - 16) = 0

x + 2 = 0 or x - 16 = 0

x = - 2 or x = 16

Hence, option C is correct;

x = - 2 or x = 16