Question 635898: 15x^2+2x=56
Answer by DrBeeee(684)   (Show Source):
You can put this solution on YOUR website! Firstly you want to rewrite the equation into the standard quadratic form
15x^2 + 2x - 56 = 0
Because of the coefficient of x^2 and the multiple factors of 56, only the brainiacs can quickly factor this quadratic. I recommend the tried and true method of factoring it - the quadratic equation (I also named this the Markconian Equation - after one of my students).
x1,2 =(-b +/-sqrt(b^2-4*a*c))/(2*a)
where a = 15, b = 2, c = -56
Applying the quadratic equation yield the two roots of the given quadratic;
x1,x2 = 56/30,-60/30
Based on the roots x1 and x2, the original quadratic factors into
a*(x-x1)(x-x2)
In our case we have
15*(x - 56/60)(x + 60/30)
Multiply the first parenthetical expression by 15 and using 60/30 = 2 we get the final factored form of the given quadratic
(15x - 28)(x + 2) = 15x^2 + 2x - 56
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