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Chapter 9: Q21. (page 566)

Solve the equation by completing the square. Round to the nearest tenth.

2x2+4x鈭�5=7

Short Answer

Expert verified

x=鈭�3.6,鈥�1.6are the solutions of the given equation.

Step by step solution

01

Step 1. Define the standard form of the quadratic equation.

A quadratic equation, which is written in the form, ax2+bx+c=0, where,a鈮�0 is called the standard form of the quadratic equation.

02

Step 2. Define the perfect square a+b2.

a+b2=a2+2ab+b2鈥夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌�...........1

03

Step 3. Solve the equation 2x2+4x−5=7 by completing the square.

Use (1) to solve the equation.

2x2+4x鈭�5=72x2+4x=7+52x2+2x=12x2+2x=122x2+2x=6

x2+2x1=6x2+2x1+12=6+12x+12=6+1x+12=7x+1=卤7x=鈭�1卤7

Use calculator.

x=鈭�3.645751311,鈥�1.645751311x鈮�鈭�3.6,鈥�1.6

Hence, x=鈭�3.6,鈥�1.6are the solutions of the given equation.

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Most popular questions from this chapter

State whether the given sentence is true or false. If false, replace the underlined term to make a true sentence.

A quadratic equation with a graph that has two x-intercepts has one real root.

Find the next three terms in each geometric sequence.

1000,鈥夆赌�500鈥夆赌�,鈥夆赌�250鈥夆赌�.....

Determine whether each trinomial is a perfect square trinomial. Write yes or no. If so, factor it.

x2+5x+25

Describe how the graph of the functionfx=x2鈭�3 is related to the graph fx=x2.

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

y=25x
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