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Chapter 9: Q24. (page 566)

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

2x2+5x鈭�3=0

Short Answer

Expert verified

x=鈭�3,鈥�12are 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 2x2+5x−3=0 by completing the square.

Compare the quadratic equation2x2+5x鈭�3=0with the quadratic equationax2+bx+c=0.

a=2,鈥�b=5,鈥�c=鈭�3

Substitute,a=2,鈥�b=5andc=鈭�3inx=鈭�b卤b2鈭�4ac2a.

x=鈭�5卤52鈭�42鈭�322x=鈭�5卤25+244x=鈭�5卤494x=鈭�5卤74x=鈭�5鈭�74,鈥�鈭�5+74x=鈭�124,鈥�24x=鈭�3,鈥�12

Hence, x=鈭�3,鈥�12are the solutions of the given equation.

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