You can put this solution on YOUR website! equation is 5a^2 + 20a - 20
first you factor out the greatest common factor.
looks like it might be 5.
you get:
5a^2 + 20a - 20 equals 5*(a^2 + 4a - 4)
now you multiply the coefficient of the a^2 term by the constant term to get 1 * 4 = 4.
now you look for factors of 4 that can be multiplied together to get 4 and added or subtracted from each other to get 4.
factors that can be multiplied together are 1*4 and 2*2.
factors from these possibilities that can be added together to get 4 are 2 + 2.
unfortunately, since your constant term is negative and your middle term is positive, you need factors that can be subtracted from each other to get 4.
none of the factors of 4 will do it, so you cannot factor this by the factoring method.
in that case, you resort to the quadratic formula.
your equation is:
5*(a^2 + 4a - 4)
this follows the standard form of ax^2 + bx + c = 0
it's unfortunate that your problem uses the variable a because that becomes confusing so we'll change your variable to x and your equation becomes:
5*(x^2 + 4x - 4) = 0
this follows the standard form of ax^2 + bx + c = 0
now you can use the quadratic formula.
a = 1
b = 4
c = -4
quadratic formula is x = (-b +/- sqrt(b^2-4ac))/2a
this becomes x = (-4 +/- sqrt(4^2-4*1*-4))/2
simplify this to get:
x = (-4 +/- sqrt(32))/2
you get 2 possible solutions.
x = -2 + 2*sqrt(2) and x = -2 - 2*sqrt(2)
since the square root of 2 is an irrational number, it's no wonder you couldn't factor using the factoring method.
that only works if the roots are rational.
if you have trouble finding the roots or the factors using the factoring method, then use the quadratic formula.
that will always find the roots no matter what they are.
it can also tell you whether or not you should have been able to factor the equation. if the roots are rational, then you probably could have found the roots using the factoring method.
the roots of this equation are:
x = -2 + 2*sqrt(2)
x = -2 - 2*sqrt(2)
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