SOLUTION: I am trying to solve an equation by factoring. The equation is: x^2/2 + x/20 = 10 What I have done is cleared the denominators and ended up with: 10x^2 + x = 10

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Question 667139: I am trying to solve an equation by factoring. The equation is:
x^2/2 + x/20 = 10
What I have done is cleared the denominators and ended up with:
10x^2 + x = 10
Then I moved the 10 to the left side of the equation and ended up with:
10x^2 + x -10 = 0
I am stuck and cannot factor: 10x^2 + x -10
The answer in the back of the book is: {2/5, -1/2}, but am not sure how to get to this answer without successfully factoring first.
In an attempt to factor, I multiplied the first and last coefficients and came up with -100. There are no numbers that when multiplied together equal -100 and also equal the middle coefficient of 1 when added together.
Please help.
Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website!

You are not simply changing the appearance
of the fractions on the left side. This would be
the case if you did:

Note that you haven't really changed the value
of the left side

Now you can multiply through by

--------------------------
What you wanted to do was multiply both sides by

same answer

You can use the quadratic formula

and

check:

Multiply both sides by

OK
Why does the book disagree? I don't know