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

1 Answer
Mar 20, 2016

Answer:

#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|#