Question

8x^2+36x+30=10-x^2Round your answer to the nearest hundreth or write them as a fraction

Answer 1

`\begin{gathered} 8x^2+36x+30=10-x^2 \\ \end{gathered}`

Solve for x:

`\begin{gathered} 8x^2+36x+30+x^2-10=0 \\ 9x^2+36x+20=0 \end{gathered}`

Factor:

`\begin{gathered} 9x^2+36x+20=(3x+2)(3x+10) \\ so\colon \\ (3x+2)(3x+10)=0 \end{gathered}`

Split into 2 equations:

`\begin{gathered} 3x+2=0_{\text{ }}(1) \\ 3x+10=0_{\text{ }}(2) \end{gathered}`

For (1):

`\begin{gathered} 3x=-2 \\ x=-(2)/(3) \end{gathered}`

For (2):

`\begin{gathered} 3x=-10 \\ x=-(10)/(3) \end{gathered}`

Answer:

As a fractions:

`\begin{gathered} x=-(2)/(3) \\ or \\ x=-(10)/(3) \end{gathered}`

As a decimals:

`\begin{gathered} x\approx-0.67 \\ or \\ x\approx-3.33 \end{gathered}`