Which of the following values are solutions to the equation (x - 3)^2 = 16? Select all tha… — GRE General Test

Which of the following values are solutions to the equation $(x - 3)^2 = 16$ ? Select all that apply.

The solutions to the equation are

-1

and

7

Taking the square root of both sides of

(x - 3)^2 = 16

gives

x - 3 = 4

x - 3 = -4

. Solving these equations yields

x = 7

and

x = -1

Take the square root of both sides of the quadratic equation

(x - 3)^2 = 16

x - 3 = \pm \sqrt{16} = \pm 4

Applying the square root property yields both a positive and a negative root.

Solve the equation corresponding to the positive root:

x - 3 = 4

x = 4 + 3 = 7

Adding

3

to both sides isolates

x

Solve the equation corresponding to the negative root:

x - 3 = -4

x = -4 + 3 = -1

Adding

3

to both sides isolates

x

for the negative root.

Solving quadratic equations of the form

(x - a)^2 = k

using the square root property.

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