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
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