SOLUTION: solve quadratic equation by factoring x^2+15x=-50

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Question 1193600: solve quadratic equation by factoring
x^2+15x=-50
Found 2 solutions by greenestamps, josgarithmetic:
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


x%5E2%2B15x=-50

(1) Get all terms on one side of the equation (add 50 to both sides):

x%5E2%2B15x%2B50=0

(2) You want to factor this as the product of two linear expressions. The constant term is positive, so the signs of the two expressions are the same; and the linear term is positive, so the signs of the two expressions are both positive. So the factoring will be of the form

%28x%2Ba%29%28x%2Bb%29=x%5E2%2B%28a%2Bb%29x%2Bab=x%5E2%2B15x%2B50

So you want a and b to be two positive integers whose sum is 15 and whose product is 50 -- 5 and 10. So

x%5E2%2B15x%2B50=%28x%2B5%29%28x%2B10%29=0
The product is 0 if and only if one of the factors is 0:

x%2B5=0 --> x=-5 or x%2B10=0 --> x=-10

ANSWERS: x=-5 and x=-10

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
By FACTORING,
x^2+15x=-50
x(x+15)=-50
Factorizations for 50:
2%2A25=5%2A10
But for two numbers to give -50, and they differ each other by 15, look at either
-5 and 10
or
5 and -10.

If x=-5, then x+15=-5+15=10.
You could check to see if the other combination does or does not also work.