SOLUTION: Find the roots of x^2+11x =-30 I need the steps please and thank you.

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Question 761571: Find the roots of x^2+11x =-30
I need the steps please and thank you.
Answer by ramkikk66(644) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2+%2B+11%2Ax+=+-30
Can be written as:
x%5E2+%2B+11%2Ax+%2B+30+=+0
If the two roots are -a and -b, then (x + a)*(x + b) = 0
x^2 + (a+b) x + ab = 0.
Comparing it with your equation,
a + b = 11
a * b = 30
One way to find out a and b is through trial and error, by looking at all factors of 30 that sum up to 11. We get the combination of 6 and 5.
So the equation can be written as
x%5E2+%2B+6%2Ax+%2B+5%2Ax+%2B+30+=+0
x+%2A+%28x+%2B+6%29+%2B+5+%2A+%28x+%2B+6%29+=+0
%28x+%2B+6%29+%2A+%28x+%2B+5%29+=+0
+x+=+-6+ or +x+=+-5
Roots are -6 and -5.
You can also solve it using the standard quadratic solver.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B11x%2B30+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%2811%29%5E2-4%2A1%2A30=1.

Discriminant d=1 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-11%2B-sqrt%28+1+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2811%29%2Bsqrt%28+1+%29%29%2F2%5C1+=+-5
x%5B2%5D+=+%28-%2811%29-sqrt%28+1+%29%29%2F2%5C1+=+-6

Quadratic expression 1x%5E2%2B11x%2B30 can be factored:
1x%5E2%2B11x%2B30+=+1%28x--5%29%2A%28x--6%29
Again, the answer is: -5, -6. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B11%2Ax%2B30+%29