Chapter 9: Q32. (page 594)

Solve each equation by completing the square. Round to the nearest tenth if necessary.
$- a^{2} - 10 a + 25 = 25$

Short Answer

Expert verified

Thesolutions of the quadratic equations are 0 and $- 10$ .

Step by step solution

Step 1. Complete the square.

Complete the square to solve the quadratic equations by isolating $x^{2}$ andbx-terms.

role="math" localid="1647844845483" $- a^{2} - 10 a + 25 = 25 \frac{- a^{2} - 10 a + 25}{- 1} = \frac{25}{- 1} a^{2} + 10 a - 25 = - 25 a^{2} + 10 a - 25 + 25 = - 25 + 25 [ add25 to each side ] a^{2} + 10 a + 25 = 25 [Since {(\frac{10}{2})}^{2} = 25 add to each side]$

Step 2. Take the square root of each side.

The first factor $a^{2} + 10 a + 25$ , then take the square root of each side.

$a^{2} + 10 a + 25 = 25 {(a + 5)}^{2} = 25 \sqrt{{(a + 5)}^{2}} = \pm \sqrt{25} a + 5 = \pm 5$

Step 3. Write the solutions.

Now subtract 5 from both sides and separate the solutions.

$- 5 + a + 5 = - 5 \pm 5$

$a = - 5 \pm 5 a = - 5 + 5 or a = - 5 - 5 a = 0 or a = - 10$

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Solve each equation by completing the square. Round to the nearest tenth if necessary.
$- a^{2} - 10 a + 25 = 25$

Short Answer

Step by step solution

Step 1. Complete the square.

Step 2. Take the square root of each side.

Step 3. Write the solutions.

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Solve each equation by completing the square. Round to the nearest tenth if necessary.−a2−10a+25=25

Short Answer

Step by step solution

Step 1. Complete the square.

Step 2. Take the square root of each side.

Step 3. Write the solutions.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Discrete Mathematics

Decision Maths

Geometry

Logic and Functions

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Solve each equation by completing the square. Round to the nearest tenth if necessary.
$- a^{2} - 10 a + 25 = 25$