Question

Complete the square to solve the equation below.
x^2 + 2x - 14 = 10

A. x = 5; x = -4
B. x = -6; x = 4
C. x = -1; x = 4
D. x = -1; x = 3

Answer 1

To complete the square :
\[x^2 +bx = c\]
\[x^2 +bx + (\frac{b}{2})^2 = c + (\frac{b}{2})^2\]
\[(x+ \frac{b}{2})^2 = c+ (\frac{b}{2})^2\]
\[x + \frac{b}{2} =\pm \sqrt{c+ (\frac{b}{2})^2}\]
\[x =- \frac{b}{2} \pm \sqrt{c+ (\frac{b}{2})^2}\]

Answer 2

In this example,
b = 2
c = 10+14 = 24