Math Word Problems Demystified - A Self Teaching Guide

EXAMPLE:Find the solution to 2xþx^2 ¼8.

SOLUTION:

Step 1: Write the equation in standard form

x^2 þ 2 x
 8 ¼ 0

Step 2: Factor the left member

ðxþ 4 Þðx
 2 Þ¼ 0

Step 3: Set each factor to zero

xþ 4 ¼0 and x
 2 ¼ 0

Step 4: Solve each equation

xþ 4 ¼ 0 x
 2 ¼ 0

xþ 4 
 4 ¼ 0 
 4 x
 2 þ 2 ¼ 0 þ 2

x¼
 4 x¼ 2

Notice that there are two solutions. You can check each value.

x¼
 4 : 2 xþx^2 ¼ 8

2 ð
 4 Þþð
 4 Þ^2 ¼ 8

 8 þ 16 ¼ 8

8 ¼ 8

x¼ 2 : 2 xþx^2 ¼ 8

2 ð 2 Þþ 22 ¼ 8

4 þ 4 ¼ 8

8 ¼ 8

EXAMPLE:Solve 2x^2
5 ¼ 3 x.

REFRESHER VI Quadratic Equations 227