Question

Solve x 2 + 9x + 8 = 0 by completing the square. What are the solutions? (1.-8) {1,8] {-1-8)

Answer 1

Given the quadratic equation:

`x^2+9x+8`

To solve it you have to use the quadratic formula

`x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}`

For the given function the coefficients are:

a=1

b=9

c=8

Replace them in the formula:

`\begin{gathered} x=\frac{-9\pm\sqrt[]{(9)^2-4\cdot1\cdot8}}{2\cdot1} \\ x=\frac{-9\pm\sqrt[]{81-32}}{2} \\ x=\frac{-9\pm\sqrt[]{49}}{2} \end{gathered}`

Now you have to calculate it using separate ways.

Positive:

`\begin{gathered} x=\frac{-9+\sqrt[]{49}}{2} \\ x=(-9+7)/(2) \\ x=(2)/(2) \\ x=1 \end{gathered}`

Negative:

`\begin{gathered} x=\frac{-9-\sqrt[]{49}}{2} \\ x=(-9-7)/(2) \\ x=-(16)/(2) \\ x=-8 \end{gathered}`

The possible values for x are 1 and -8, the correct option is the first one.