#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|#
