Question

Solve the quadratic equation x2 – 10x + 14 = –4 by completing the square.

Question 3 options:

A)

x = 5 ±

B)

x = –5 ±

C)

x = –7 ±

D)

x = 7 ±

Answer 1

`x = 5 \pm √(7)`

Explanation:

x^2 - 10x + 14 = -4

Subtract 14 from both sides.

x^2 - 10x = -18

To complete the square, add the square of half of the x-term's coefficient.

x-term coefficient: -10

half of it: -5

squared: (-5)^2 = 25

Add 25 to both sides.

x^2 - 10x + 25 = -18 + 25

(x - 5)^2 = 7

Take square root of both sides. Be careful to include ± on the right side.

`x - 5 = \pm √(7)`

Add 5 to both sides.

`x = 5 \pm √(7)`