SOLUTION: 5x^2-5x=150 found solution using quadratic equation to be 6 and -5. 6^2=36 5*36=180 5*6=30 180-30=150 Use solution in original equation, 6 works, but for

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: 5x^2-5x=150 found solution using quadratic equation to be 6 and -5. 6^2=36 5*36=180 5*6=30 180-30=150 Use solution in original equation, 6 works, but for       Log On


   

Question 705265: 5x^2-5x=150 found solution using quadratic equation to be 6 and -5.
6^2=36 5*36=180
5*6=30
180-30=150
Use solution in original equation, 6 works, but for the life of me I cannot figure out what I am doing wrong with the -5 solution.
-5^2=-25 -25*5=-125
Thanks
5*-5=-25
-125 --25=100
Answer by jsmallt9(3759) About Me  (Show Source):
You can put this solution on YOUR website!
6 and -5 are the correct solutions.

When you check -5 as a solution you are supposed to replace the x's in:
5x%5E2-5x=150
with a -5. In the first term, the x is being squared. So when we replace it with -5, the -5 should be squared, too. A proper replacement of the x's with 6's and -5's would look like:
5%286%29%5E2-5%286%29=150
and
5%28-5%29%5E2-5%28-5%29=150
Notice the parentheses!! They make little difference with the replacements with 6's. But they are critical when replacing the x's with -5! So it is an extremely good habit to use parentheses when making substitutions.

Your mistake was not using the parentheses and then finding
-5^2
which means "the negative of 5 squared" which is, of course, -25.
What you should have been doing was
(-5)^2
which means "the square of -5" which is, of course, 25. With a 25 instead of -25 you will find that -5 does check out.