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Chapter 9: Q32. (page 594)

Solve each equation by completing the square. Round to the nearest tenth if necessary.

鈭�a2鈭�10a+25=25

Short Answer

Expert verified

Thesolutions of the quadratic equations are 0 and-10.

Step by step solution

01

Step 1. Complete the square.

Complete the square to solve the quadratic equations by isolating x2 andbx-terms.

role="math" localid="1647844845483" 鈭�a2鈭�10a+25=25鈭�a2鈭�10a+25鈭�1=25鈭�1a2+10a鈭�25=鈭�25a2+10a鈭�25+25=鈭�25+25鈥夆赌夆赌夆赌塠鈥夆赌塧诲诲25鈥夆赌塼辞鈥夆赌塭补肠丑鈥夆赌塻颈诲别鈥夆赌坞鈥夆赌�a2+10a+25=25鈥夆赌夆赌夆赌�[鈥夆赌塖颈苍肠别鈥夆赌�1022=25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鈥夆赌�]

02

Step 2. Take the square root of each side. 

The first factor a2+10a+25, then take the square root of each side.

a2+10a+25=25a+52=25a+52=卤25a+5=卤5

03

Step 3. Write the solutions.

Now subtract 5 from both sides and separate the solutions.

鈭�5+a+5=鈭�5卤5

a=鈭�5卤5a=鈭�5+5鈥夆赌夆赌夆赌夆�夆�塷r鈥夆�夆��a=鈭�5鈭�5a=0鈥夆赌夆赌夆赌夆�塷r鈥夆赌夆赌夆赌�a=鈭�10

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Most popular questions from this chapter

Graph each function. Find the y-intercept, and state the domain and range.

y=3x+1

Solve the equation by using the Quadratic formula. Round to the nearest tenth if necessary.

x2鈭�10x=鈭�15

Question: Find the vertex, the equation of the axis of symmetry, and the y-intercept of the given equation.

y=2x2鈭�12x+6

Use a table of values to graph the given equation. State the domain and range.

y=鈭�3x2鈭�x+1

Which is an equation for the function shown in the graph?

Ay=鈭�2x2

By=2x2+1

Cy=x2鈭�1

Dy=鈭�2x2+1
See all solutions

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