Question

Solve by completing the squareX^2 + 6x + 8 = 0

Answer 1

x = - 4, x = - 2

Explanation:

x² + 6x + 8 = 0 ( subtract 8 from both sides )

x² + 6x = - 8

to complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(3)x + 9 = - 8 + 9

(x + 3)² = 1 ( take square root of both sides )

x + 3 = ±
`√(1)` = ± 1 ( subtract 3 from both sides )

x = - 3 ± 1

Then

x = - 3 - 1 = - 4

x = - 3 + 1 = - 2

Answer 2

Solve by completing the square:

`\begin{gathered} x^2+6x+8=0 \\ x^2+6x=-8 \end{gathered}`

We have to find the third term for x^2+6x in order to complete a binomial (x+3)^2:

`(x+3)^2=x^2+2\cdot3x+9=x^2+6x+9`

So we have to add 9:

`\begin{gathered} x^2+6x+9=-8+9 \\ (x+3)^2=1 \end{gathered}`

Then, we apply the square root:

`\begin{gathered} \sqrt[]{(x+3)^2}=\sqrt[]{1} \\ x+3=\pm1 \end{gathered}`
`\begin{gathered} x_1+3=-1 \\ x_1=-1-3=-4 \end{gathered}`
`\begin{gathered} x_2+3=+1 \\ x_2=1-3=-2 \end{gathered}`

Answer: The solutions are x=-4 and x=-2