Question

Solve the equation by factoring. Check your answer by graphing.

x² - 4x = 5
Step 1 - Write the equation in the form x² + bx + c = 0.
4.
Step 2 Factor and solve the equation using the Zero Product Property.
Step 3 Graph the related function (x) = x² + bx + c.
The related function is f(x) =
x
f(x)
1
The solutions of the equation are x =
and x =
-7 -6
Y
Pairs of
Factors for
C =
6
5
4
3
2
1
--3-2-10 1
-2
-3
4
-5
2
Sum of
Factors
b
3
4
5
?
6

Answer 1

Both factor method and graphing give the same solutions of x = -1 and x = 5.

How to solve quadratic equation

Given

x² - 4x = 5

Step1: In the form x² + bx + c = 0 is

Subtract 5 from both sides

x² - 4x - 5 = 5 - 5

x² - 4x - 5 = 0

Step 2 : Using the zero product property

Pair of factors of -5 Sum of factors (-4)

1 and 5 6

-1 and -5 -6

1 and -5 -4

-1 and 5 4

So, 1 and -5 satisfy the product and sum of factors.

x² -5x + x - 5 = 0

x(x - 5) +1(x - 5) = 0

(x - 5)(x + 1) = 0

x - 5 = 0 or x + 1 = 0

x = 5 or x = -1

Step 3, the related equation is

y = x² - 4x -5

Table of value for y = x² - 4x -5

x y

-2 7

-1 0

0 -5

1 -8

2 -9

Plot the pairs of values on a graph and connect with smooth curve to create a graph for the quadratic equation.

The roots of the equation are the x-intercepts of curve.

They occur at x = -1 and x = 5

Therefore, both factor method and graphing give the same solutions of x = -1 and x = 5.