Solving a quadratic equation by completing the square

Question

Solve the quadratic equation by completing the square.

x^2+14x+38=0

First, choose the appropriate form and fill in the blanks with the correct numbers. Then, solve the equation. If there is more than one solution, separate them with commas.

Answer 1

x^2 + 14x = -38

x^2 + 14x + 49 = 11

(x+7)^2 = 11

x+7 = +or- sqrt(11)

x = -7 +or- sqrt(11)

check:

x = -7 + sqrt(11)

x^2 = 49 + -14*sqrt(11) + 11 = 60 - 14*sqrt(11)

14x = -98 + 14*sqrt(11)

x^2+14x - 38 = 60 -14*sqrt(11) - 98 + 14*sqrt(11) - 38

= 60 - 98 + 38

yes it checks

x = -7 +or- sqrt(11)