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viktelen [127]
3 years ago
13

Select the two values of x that are roots of this equation 2x-3=-5x^2

Mathematics
1 answer:
zvonat [6]3 years ago
3 0

\bold{Answer}

\boxed{\bold{X \ = \ -1, \ X \ = \ \frac{3}{5} }}

\bold{Explanation}

  • \bold{Find \ Two \ Values \ Of \ X: \ 2x-3=-5x^2}

\bold{-------------------}

  • \bold{Switch \ Sides}

\bold{-5x^2=2x-3}

  • \bold{Add \ 3 \ To \ Both \ Sides}

\bold{-5x^2+3=2x-3+3}

  • \bold{Simplify}

\bold{-5x^2+3=2x}

  • \bold{Subtract \ 2x \ From \ Both \ Sides}

\bold{-5x^2+3-2x=2x-2x}

  • \bold{Simplify}

\bold{-5x^2-2x+3=0}

  • \bold{Solve \ With \ The \ Quadratic \ Formula}
  • \bold{For \ The \ Quadratic \ Form \ For \ ax^2+bx+c=0 \ The \ Solutions \ Are \ x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}}
  • \bold{For \ A \ =-5,\:b=-2,\:c=3:\quad x_{1,\:2}=\frac{-\left(-2\right)\pm \sqrt{\left(-2\right)^2-4\left(-5\right)3}}{2\left(-5\right)}}

\bold{\frac{-\left(-2\right)+\sqrt{\left(-2\right)^2-4\left(-5\right)\cdot \:3}}{2\left(-5\right)}: \ -1}

\bold{\frac{-\left(-2\right)-\sqrt{\left(-2\right)^2-4\left(-5\right)\cdot \:3}}{2\left(-5\right)}: \ \frac{3}{5} }

  • \bold{Solutions}

\bold{x=-1,\:x=\frac{3}{5}}

\boxed{\bold{Eclipsed}}

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