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Chapter 9: Q19. (page 566)

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

x2+4x+2=0

Short Answer

Expert verified

x=0.6,鈥�3.4 are 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 x2+4x+2=0 by completing the square.

Use (1) to solve the equation.

x2+4x+2=0x2+2x2+2=0x2+2x2+22+2=22x+22+2=4

x+22=4鈭�2x+22=2x+2=卤2x=2卤2x=2鈭�2,鈥�2+2

Use calculator.

x=0.585786437,鈥�3.414213562x鈮�0.6,鈥�3.4

Hence, x=0.6,鈥�3.4are the solutions of the given equation.

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Most popular questions from this chapter

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