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Chapter 9: Q20. (page 566)

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

x2鈭�2x鈭�10=0

Short Answer

Expert verified

x=鈭�2.3,鈥�4.4are 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鈭�b2=a2鈭�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 x2−2x−10=0 by completing the square.

Use (1) to solve the equation.

x2鈭�2x鈭�10=0x2鈭�2x1鈭�10=0x2鈭�2x1+12鈭�10=12x鈭�12鈭�10=1

x鈭�12=1+10x鈭�12=11x鈭�1=卤11x=1卤11x=1鈭�11,鈥夆赌�1+11

Use calculator.

x=鈭�2.31662479,鈥�4.3662479x鈮�鈭�2.3,鈥�4.4

Hence, x=鈭�2.3,鈥�4.4are the solutions of the given equation.

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