[tex]\begin{gathered} 8x^2+36x+30=10-x^2 \\ \end{gathered}[/tex]
Solve for x:
[tex]\begin{gathered} 8x^2+36x+30+x^2-10=0 \\ 9x^2+36x+20=0 \end{gathered}[/tex]
Factor:
[tex]\begin{gathered} 9x^2+36x+20=(3x+2)(3x+10) \\ so\colon \\ (3x+2)(3x+10)=0 \end{gathered}[/tex]
Split into 2 equations:
[tex]\begin{gathered} 3x+2=0_{\text{ }}(1) \\ 3x+10=0_{\text{ }}(2) \end{gathered}[/tex]
For (1):
[tex]\begin{gathered} 3x=-2 \\ x=-\frac{2}{3} \end{gathered}[/tex]
For (2):
[tex]\begin{gathered} 3x=-10 \\ x=-\frac{10}{3} \end{gathered}[/tex]
Answer:
As a fractions:
[tex]\begin{gathered} x=-\frac{2}{3} \\ or \\ x=-\frac{10}{3} \end{gathered}[/tex]
As a decimals:
[tex]\begin{gathered} x\approx-0.67 \\ or \\ x\approx-3.33 \end{gathered}[/tex]
