1.4 Quadratic Equations

Solving Quadratic Equations by Factoring: Trinomial a=1

Example: Solve the quadratic equation by factoring.

x^2+x=20

Solution:

The original equation
x^2+x=20
Write the equation with all the terms on one side of the equation and zero on the other side of the equation. x^2+x=20
x^2+x-20=20-20
x^2+x-20=0
Factor the expression on one side. x^2+x-20=0
(x+5)(x-4)=0
Use the zero product property and set each factor equal to zero. (x+5)(x-4)=0
x+5=0 or x-4=0
Solve each equation. x+5=0 or x-4=0
x+5-5=0-5 or x-4+4=0+4
x=-5 or x=4

Check: x=4

x^2+x=20
(4)^2+4=20
16+4=20
20=20

Since the value of 4 makes the equation true, 4 is a solution to the equation.

Check: x=-5

x^2+x=20
(-5)^2+(-5)=20
25-5=20
20=20

Since the value of -5 makes the equation true, -5 is a solution to the equation.