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Chapter 9: Q22. (page 566)

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

x2鈭�3x鈭�18=0

Short Answer

Expert verified

x=鈭�3,鈥�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 quadratic formula.

For the quadratic equationax2+bx+c=0, where,a鈮�0 is given by

x=鈭�b卤b2鈭�4ac2a

03

Step 3. Solve the equation x2−3x−18=0 by completing the square.

Compare the quadratic equationx2鈭�3x鈭�18=0with the quadratic equationax2+bx+c=0.

a=1,鈥�b=鈭�3,鈥�c=鈭�18

Substitute,a=1,鈥�b=鈭�3andc=鈭�18inx=鈭�b卤b2鈭�4ac2a.

x=鈭�鈭�3卤鈭�32鈭�41鈭�1821x=3卤9+722x=3卤812x=3卤92x=3鈭�92,鈥�3+92x=鈭�62,鈥�122x=鈭�3,鈥�6

Hence, x=鈭�3,鈥�6are the solutions of the given equation.

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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+2

Solve each equation by graphing. If integral roots cannot be found, estimate the roots to the nearest tenth.

x2鈭�3x鈭�4=0

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

5t2鈭�12t+25

Find the next three terms of each arithmetic sequence.

3,5,7,9,...

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

y=鈭�x2鈭�3x鈭�3
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