If x is a real number that satisfies the equation (x - 3)^2 = 16, which of the following c… — GRE General Test

If $x$ is a real number that satisfies the equation $(x - 3)^2 = 16$ , which of the following could be the value of $x^2 - 4x$ ? Select all such values.

A
$-5$
$5$ Answer
$21$ Answer
D
$45$
E
$77$

Answer

The possible values of

x^2 - 4x

are

5

and

21

Taking the square root of both sides of

(x - 3)^2 = 16

yields

x - 3 = \pm 4

. This gives two solutions for

x

x = 7

and

x = -1

. Substituting

x = 7

into

x^2 - 4x

gives

49 - 28 = 21

. Substituting

x = -1

into

x^2 - 4x

gives

(-1)^2 - 4(-1) = 1 + 4 = 5

. Thus, both

5

and

21

are valid values.

Step-by-Step Solution

Solve the quadratic equation for

x

x - 3 = 4 \implies x = 7

x - 3 = -4 \implies x = -1

Taking the square root of both sides of

(x - 3)^2 = 16

yields both positive and negative roots.

Substitute the first root into the expression

x^2 - 4x

7^2 - 4(7) = 49 - 28 = 21

Evaluating the target expression for

x = 7

Substitute the second root into the expression

x^2 - 4x

(-1)^2 - 4(-1) = 1 + 4 = 5

Evaluating the target expression for

x = -1

Key Concept

Quadratic Equations and Factoring

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

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