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What number must you add to complete the square?

x^2 - 16x = 23

A. -8

B. -64

C. 64

D. 8

What number must you add to complete the square? x^2 - 16x = 23 A. -8 B. -64 C. 64 D-example-1
User NamiW
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2 Answers

6 votes
6 votes

Answer:

D

Explanation:

What number must you add to complete the square? x^2 - 16x = 23 A. -8 B. -64 C. 64 D-example-1
User Palako
by
2.7k points
21 votes
21 votes

Answer:

D. 8

Explanation:

To create a trinomial square on the left side of the equation, find a value that is equal to the square of half of b.

(b/2) ² = (-8)²

Add the term to each side of the equation.

x² - 16x + (-8)² = 23 + (-8)²

Simplify the equation.

Raise -8 to the power of 2.

x² - 16x + 64 = 23 + (-8)²

Simplify 23 - (-8)²

Raise - 8 to the power of 2.

x² - 16x + 64 = 23 + 64

Add 23 and 64

x² - 16x + 64 = 87

Factor the perfect trinomial square into (x-8)²

(x-8)²=87

Solve the equation for x.

Take the square root of each side of the equation to set up the solution for x.

(x-8)²*¹/₂ = ±√87

Remove the perfect root factor x-8 under the radical to solve for x.

x - 8 = ±√87

Remove parentheses.

x - 8 = ±√87

Add 8 to both sides of the equation.

x = ±√87 + 8

The result can be shown in multiple forms.

Exact Form:

x = ±√87 + 8

Decimal Form:

x=17.32737905…,−1.32737905…

User UIAdam
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2.4k points