# How do you solve  2x^2-x-10=0?

Mar 20, 2016

$x = - 2 , \frac{5}{2}$

#### Explanation:

color(blue)(2x^2-x-10=0

We can solve the equation by factoring and also by Quadratic formula

$\approx \approx \approx \approx \approx \approx \approx \approx \approx \approx \approx \approx \approx \approx \approx \approx \approx \approx$

Factoring

Factor the equation

$\rightarrow \left(2 x - 5\right) \left(x + 2\right) = 0$

If we solve for it we get color(green)(x=-2,5/2

$\approx \approx \approx \approx \approx \approx \approx \approx \approx \approx \approx \approx \approx \approx \approx \approx \approx \approx$

This is a Quadratic equation (in form $a {x}^{2} + b x + c = 0$)

color(brown)(x=(-b+-sqrt(b^2-4ac))/(2a)

Where

color(red)(a=2,b=-1,c=-10

$\rightarrow x = \frac{- \left(- 1\right) \pm \sqrt{- {1}^{2} - 4 \left(2\right) \left(- 10\right)}}{2 \left(2\right)}$

$\rightarrow x = \frac{1 \pm \sqrt{1 - \left(- 80\right)}}{4}$

$\rightarrow x = \frac{1 \pm \sqrt{1 + 80}}{4}$

$\rightarrow x = \frac{1 \pm \sqrt{81}}{4}$

$\Rightarrow x = \frac{1 \pm 9}{4}$

Now we have two solutions

color(orange)(rArrx= (1+9)/(4)=10/2=5/2

color(indigo)(rArrx=(1-9)/(4)=-8/4=-2

$\approx \approx \approx \approx \approx \approx \approx \approx \approx \approx \approx \approx \approx \approx \approx \approx \approx$

color(blue)( :.ul bar |x=-2,5/2|