Question

What are the two solutions of 2x^2=-x^2-5x-1

Answer 1

x = 5/-6 + (√13)/-6

x = 5/-6 -(√13)/-6

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.

Answer 2

`Solution, 2x^2=-x^2-5x-1: x=-(5+√(13))/(6),\:x=-(5-√(13))/(6)`

`Steps:`

`2x^2=-x^2-5x-1`

`\mathrm{Switch\:sides},\\-x^2-5x-1=2x^2`

`\mathrm{Subtract\:}2x^2\mathrm{\:from\:both\:sides},\\-x^2-5x-1-2x^2=2x^2-2x^2`

`\mathrm{Simplify},\\-3x^2-5x-1=0`

`Solve\:with\:the\:quadratic\:formula,\\\mathrm{For\:}\quad a=-3,\:b=-5,\:c=-1:\quad x_(1,\:2)=(-\left(-5\right)\pm √(\left(-5\right)^2-4\left(-3\right)\left(-1\right)))/(2\left(-3\right))\\x=(-\left(-5\right)+√(\left(-5\right)^2-4\left(-3\right)\left(-1\right)))/(2\left(-3\right)):\quad -(5+√(13))/(6),\\x=(-\left(-5\right)-√(\left(-5\right)^2-4\left(-3\right)\left(-1\right)))/(2\left(-3\right)):\quad -(5-√(13))/(6)`

`\mathrm{The\:final\:solutions\:to\:the\:quadratic\:equation\:are:}\\x=-(5+√(13))/(6),\:x=-(5-√(13))/(6)`

`Hope\:This\:Helps!!!`

`-Austint1414`