Answer:
[tex]\mathrm{The\:solutions\:to\:the\:quadratic\:equation\:are:}[/tex]
[tex]x=2,\:x=-8[/tex]
Step-by-step explanation:
The given expression is [tex]x^{2}+6x-6=10[/tex]
we need to solve this expression for the value of x
[tex]\mathrm{Subtract\:}10\mathrm{\:from\:both\:sides}[/tex]
[tex]\mathrm{Solve\:with\:the\:quadratic\:formula}[/tex]
[tex]\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}[/tex]
[tex]x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]\mathrm{For\:}\quad a=1,\:b=6,\:c=-16:\quad x_{1,\:2}=\frac{-6\pm \sqrt{6^2-4\cdot \:1\left(-16\right)}}{2\cdot \:1}[/tex]
[tex]x=\frac{-6+\sqrt{6^2-4\cdot \:1\left(-16\right)}}{2\cdot \:1}:\quad 2[/tex]
[tex]x=\frac{-6-\sqrt{6^2-4\cdot \:1\left(-16\right)}}{2\cdot \:1}:\quad -8[/tex]
[tex]\mathrm{The\:solutions\:to\:the\:quadratic\:equation\:are:}[/tex]
[tex]x=2,\:x=-8[/tex]
