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Chapter 10: Q 383 (page 1063)

In the following exercises,solve each equation.

5x2+2x=15.

Short Answer

Expert verified

The solution isx=-1

Step by step solution

01

Step 1.Given information

Consider the given quadratic equation5x2+2x=15

Solve the equation for x as follows;

02

Step 2.First write both sides of the equation with the same base

Because left side of the equation has base 5,so write the right side of the equation with base 5 as

5x2+2x=5-1[15=5-1]

Because the base are same 5,so the exponent must be equal.

x2+2x=-1

03

Step 3.Now solve the equation

x2+2x+1=-1+1x2+2x+1=0(x+1)2=0 x=-1So,thevalueofx=-1

04

Step 4.Check

To check the solution,replace x by -1 in original equation.

5x2+2x=155(-1)2+2(-1)=155-1=1515=15[true]Therefore,thevalueofx=15

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