Answer:
x = 5/-6 + (√13)/-6
x = 5/-6 -(√13)/-6
Step-by-step explanation:
2x^2 = -x^2 - 5x - 1. Subtract 2x^2 from both sides.
-3x^2 - 5x - 1. Do the quadratic formula.
That gives you:
-5/6 ± (√13)/-6.
[tex]Solution, 2x^2=-x^2-5x-1: x=-\frac{5+\sqrt{13}}{6},\:x=-\frac{5-\sqrt{13}}{6}[/tex]
[tex]Steps:[/tex]
[tex]2x^2=-x^2-5x-1[/tex]
[tex]\mathrm{Switch\:sides},\\-x^2-5x-1=2x^2[/tex]
[tex]\mathrm{Subtract\:}2x^2\mathrm{\:from\:both\:sides},\\-x^2-5x-1-2x^2=2x^2-2x^2[/tex]
[tex]\mathrm{Simplify},\\-3x^2-5x-1=0[/tex]
[tex]Solve\:with\:the\:quadratic\:formula,\\\mathrm{For\:}\quad a=-3,\:b=-5,\:c=-1:\quad x_{1,\:2}=\frac{-\left(-5\right)\pm \sqrt{\left(-5\right)^2-4\left(-3\right)\left(-1\right)}}{2\left(-3\right)}\\x=\frac{-\left(-5\right)+\sqrt{\left(-5\right)^2-4\left(-3\right)\left(-1\right)}}{2\left(-3\right)}:\quad -\frac{5+\sqrt{13}}{6},\\x=\frac{-\left(-5\right)-\sqrt{\left(-5\right)^2-4\left(-3\right)\left(-1\right)}}{2\left(-3\right)}:\quad -\frac{5-\sqrt{13}}{6}[/tex]
[tex]\mathrm{The\:final\:solutions\:to\:the\:quadratic\:equation\:are:}\\x=-\frac{5+\sqrt{13}}{6},\:x=-\frac{5-\sqrt{13}}{6}[/tex]
[tex]Hope\:This\:Helps!!![/tex]
[tex]-Austint1414[/tex]
