Question

What equation results from completing the square and then factoring x^2+4x=5

Answer 1

x2+4x=5
x*x*x+4=5
3x=5-4
3x=1
x=1/3

Answer 2

Equation after factoring (x +2)² - 9 = 0 and factors are x = 1 , -5 .

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 +
`(2)/(2)` *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 =
`√(9)`.

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 .