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

1 Answer
turksvids
Dec 21, 2017

−4

Explanation:

Start with 3x(x+4)=66

divide through by 3:

x(x+4)=22

expand the left side:

x2+4x=22

subtract 22 from both sides:

x2+4x−22=0.

Use the quadratic formula: x=−b±√b2−4ac2a:

x=−4+√42−4(1)(−22)2=−2+√26 or x=−4−√42−4(1)(−22)2=−2−√26

If we add those together the radicals cancel out:

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

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