Which of the following values are solutions to the equation (x + 4)^2 = 49? Select all tha… — GRE General Test

Which of the following values are solutions to the equation $(x + 4)^2 = 49$ ? Select all that apply.

The correct solutions are

-11

and

3

Taking the square root of both sides of

(x + 4)^2 = 49

yields

x + 4 = 7

x + 4 = -7

. Solving these two linear equations gives

x = 3

and

x = -11

. Both values satisfy the original quadratic equation.

Apply the square root property to both sides of the quadratic equation.

x + 4 = \pm \sqrt{49} = \pm 7

Taking the square root of both sides accounts for both the positive and negative roots of

49

Solve the first linear equation for the positive case.

x + 4 = 7 \implies x = 7 - 4 = 3

Subtract

4

from both sides when the expression equals

+7

Solve the second linear equation for the negative case.

x + 4 = -7 \implies x = -7 - 4 = -11

Subtract

4

from both sides when the expression equals

-7

Square Root Property of Quadratic Equations

Question