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Chapter 9: Q31. (page 594)

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

x2+6x+9=16

Short Answer

Expert verified

Thesolutions of the quadratic equations are 1 and-7.

Step by step solution

01

Step 1. Complete the square.

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

x2+6x+9=16x2+6x+9鈭�9=16鈭�9鈥夆赌夆赌夆赌塠鈥夆赌塻耻产迟谤补肠迟鈥夆赌�9鈥夆赌塮谤辞尘鈥夆赌塭补肠丑鈥夆赌塻颈诲别鈥夆赌坞鈥夆赌�x2+6x+9=7+9鈥夆赌夆赌夆赌夆赌�[鈥夆赌塖颈苍肠别鈥夆赌�622=9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 x2+6x+9, then take the square root of each side.

x+32=16(x+3)2=卤16x+3=卤4

03

Step 3. Write the solutions.

Now subtract 3 from both sides and separate the solutions.

x+3鈭�3=鈭�3卤4x=鈭�3+4鈥夆赌夆赌夆赌夆赌夆�塷r鈥夆�夆��x=鈭�3鈭�4x=1鈥夆赌夆赌夆赌塷谤鈥夆赌夆赌夆赌�x=鈭�7

Therefore, the solutions are 1 and -7.

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Most popular questions from this chapter

Graph鈭�2,4,鈭�1,1,0,0,1,1,2,4. Determine whether the ordered pairs represent a linear function, a quadratic function, or an exponential function.

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x2鈭�x鈭�30=0

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a. Write a system of equations to model the situation.

b. Solve the system of equations. How much does each item cost?
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