SOLUTION: solve by completing the square x^2+7x-30=0 what is the solution for x?? use commas to separate as needed

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: solve by completing the square x^2+7x-30=0 what is the solution for x?? use commas to separate as needed      Log On


   

Question 353789: solve by completing the square
x^2+7x-30=0
what is the solution for x?? use commas to separate as needed
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2+%2B+7x+-+30+=+0
Add 30 to both sides
x%5E2+%2B+7x+=+30
Take 1/2 of 7, square it, and
add it to both sides
x%5E2+%2B+7x+%2B+%287%2F2%29%5E2+=+30+%2B+%287%2F2%29%5E2
x%5E2+%2B+7x+%2B+49%2F4+=+30+%2B+49%2F4
x%5E2+%2B+7x+%2B+49%2F4+=+120%2F4+%2B+49%2F4
x%5E2+%2B+7x+%2B+49%2F4+=+169%2F4
%28x+%2B+7%2F2%29%5E2+=+%2813%2F2%29%5E2
Both sides are now perfect squares. The
right side doesn't have to be a perfect
square, but the solution is neater if it is.
Now take the square root of both sides
x+%2B+7%2F2+=+13%2F2
x+=+13%2F2+-+7%2F2
x+=+6%2F2
x+=+3
Taking the (-) square root:
x+%2B+7%2F2+=+-13%2F2
x+=+-13%2F2+-+7%2F2
x+=+-20%2F2
x+=+-10
From these I get x+-+3+=+0
and x+%2B+10+=+0
%28x+-+3%29%2A%28x+%2B+10%29+=+x%5E2+%2B+7x+-+30