Q13. Solve each equation by completin... [FREE SOLUTION]

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Algebra 1

Carter, Cuevas, Day, Holiday, Luchin

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 801 pages

ISBN: 9780078884801

Chapter 9: Q13. (page 597)

Solve each equation by completing the square.
$x^{2} 鈭� x 鈭� 6 = 0$

Short Answer

Expert verified

The solutions of the quadratic equation are $- 2$ and 3.

Step by step solution

Step 1. Complete the square

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

$x^{2} 鈭� x 鈭� 6 = 0 x^{2} 鈭� x 鈭� 6 + \frac{1}{4} = 0 + \frac{1}{4} 鈥夆赌夆赌夆赌夆赌夆赌夆赌夆赌� [厂颈苍肠别鈥夆赌� {(\frac{1}{2})}^{2} = \frac{1}{4} 鈥夆赌塧诲诲鈥夆赌塼辞鈥夆赌塭补肠丑鈥夆赌塻颈诲别] x^{2} 鈭� x + \frac{1}{4} 鈭� 6 + 6 = \frac{1}{4} + 6 鈥夆赌夆赌夆赌夆赌夆赌夆赌夆赌� [鈥碱诲诲鈥夆赌�6鈥夆赌塼辞鈥夆赌塭补肠丑鈥夆赌塻颈诲别鈥�] x^{2} 鈭� x + \frac{1}{4} = \frac{25}{4}$

Step 2. Take the square root of each side

First factor $x^{2} 鈭� x + \frac{1}{4}$ , then take square root of each side.

${(x 鈭� \frac{1}{2})}^{2} = \frac{25}{4} \sqrt{{(x 鈭� \frac{1}{2})}^{2}} = 卤 \sqrt{\frac{25}{4}} x 鈭� \frac{1}{2} = 卤 \frac{5}{2}$

Step 3. Write the solutions

Add $\frac{1}{2}$ to both sides and separate the solutions.

$x 鈭� \frac{1}{2} + \frac{1}{2} = \frac{1}{2} 卤 \frac{5}{2} x = \frac{1}{2} 鈭� \frac{5}{2} 鈥夆赌夆赌夆赌夆赌夆赌塷谤鈥夆赌夆赌夆赌夆赌� x = \frac{1}{2} + \frac{5}{2} x = 鈭� 2 鈥夆赌夆赌夆赌塷谤鈥夆赌� x = 3$

Therefore, the solutions of the equation are $- 2$ and 3.

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91影视

Solve each equation by completing the square.
$x^{2} 鈭� x 鈭� 6 = 0$

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.

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91影视

Solve each equation by completing the square.x2鈭�x鈭�6=0

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

Mechanics Maths

Calculus

Logic and Functions

Applied Mathematics

Theoretical and Mathematical Physics

Statistics

Study anywhere. Anytime. Across all devices.

Solve each equation by completing the square.
$x^{2} 鈭� x 鈭� 6 = 0$