Answer:
Equation after factoring (x +2)² - 9 = 0 and factors are x = 1 , -5 .
Step-by-step explanation:
Given : x²+4x=5.
To find : what equation results from completing the square and then factoring.
Solution : We have given
x² + 4x = 5.
On subtracting both sides by 5
x² + 4x - 5 = 0.
multiply and divide the second term 4x by 2
x² + [tex]\frac{2}{2}[/tex] *4x - 5 = 0.
x² + 2 * 2x - 5 = 0.
Now, adding and subtracting by 4
x² + 2 * 2x + 4 -4 - 5 = 0.
We can see x² + 2 * 2x + 4 is the complete square of (x +2)².
Then
(x +2)² -4 - 5 = 0.
(x +2)² - 9 = 0.
Now adding both sides by 9
(x +2)² = 9.
Taking square root both sides.
x + 2 = [tex]\sqrt{9}[/tex].
x + 2 = ± 3.
We will take both case
For + 3
x +2 = 3
On subtracting both sides by 2
x = 3-2
x = 1 .
For x + 2 = -3.
On subtracting both sides by 2
x = -3 -2
x = -5 .
Factors are x = 1 , -5 .
Therefore, Equation after factoring (x +2)² - 9 = 0 and factors are x = 1 , -5 .
