Find The Sum Of All Solutions To The Equation 3x(x+4)=66. Help, Please?

1 Answer
Dec 21, 2017

-4

Explanation:

Start with 3x(x+4)=66

divide through by 3:

x(x+4)=22

expand the left side:

x^2+4x=22

subtract 22 from both sides:

x^2+4x-22=0.

Use the quadratic formula: x=(-b\pmsqrt(b^2-4ac))/(2a):

x=(-4+sqrt(4^2-4(1)(-22)))/(2)=-2+sqrt(26) or x=(-4-sqrt(4^2-4(1)(-22)))/(2)=-2-sqrt(26)

If we add those together the radicals cancel out:

-2+sqrt(26) +(-2-sqrt(26)) = -4, which is just actually the opposite of b/a: sum of roots is -b/a, but most of my students never remember that so they go through all the work I just did.