Question

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

Answer 1

`x=-2,5/2`

Explanation:

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

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

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Factoring

Factor the equation

`rarr(2x-5)(x+2)=0`

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

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Quadratic formula

This is a Quadratic equation (in form `ax^2+bx+c=0`)

Use Quadratic formula

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

Where

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

`rarrx=(-(-1)+-sqrt(-1^2-4(2)(-10)))/(2(2))`

`rarrx=(1+-sqrt(1-(-80)))/(4)`

`rarrx=(1+-sqrt(1+80))/(4)`

`rarrx=(1+-sqrt81)/(4)`

`rArrx=(1+-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`

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