SOLUTION: Use the quadratic formula to solve: 5x^2+12=-6x

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Question 179010This question is from textbook
: Use the quadratic formula to solve: 5x^2+12=-6x This question is from textbook

Found 2 solutions by Mathtut, jim_thompson5910:
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
5x%5E2%2B6x%2B12=0
:
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 5x%5E2%2B6x%2B12+=+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=%286%29%5E2-4%2A5%2A12=-204.

The discriminant -204 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.


In the field of imaginary numbers, the square root of -204 is + or - sqrt%28+204%29+=+14.2828568570857.

The solution is , or
Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B6%2Ax%2B12+%29

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

5x%5E2%2B6x%2B12=0 Start with the given equation.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=5, b=6, and c=12


Let's use the quadratic formula to solve for x


x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


x+=+%28-%286%29+%2B-+sqrt%28+%286%29%5E2-4%285%29%2812%29+%29%29%2F%282%285%29%29 Plug in a=5, b=6, and c=12


x+=+%28-6+%2B-+sqrt%28+36-4%285%29%2812%29+%29%29%2F%282%285%29%29 Square 6 to get 36.


x+=+%28-6+%2B-+sqrt%28+36-240+%29%29%2F%282%285%29%29 Multiply 4%285%29%2812%29 to get 240


x+=+%28-6+%2B-+sqrt%28+-204+%29%29%2F%282%285%29%29 Subtract 240 from 36 to get -204


x+=+%28-6+%2B-+sqrt%28+-204+%29%29%2F%2810%29 Multiply 2 and 5 to get 10.


x+=+%28-6+%2B-+2i%2Asqrt%2851%29%29%2F%2810%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%28-6%2B2i%2Asqrt%2851%29%29%2F%2810%29 or x+=+%28-6-2i%2Asqrt%2851%29%29%2F%2810%29 Break up the expression.


x+=+%28-3%2Bi%2Asqrt%2851%29%29%2F%285%29 or x+=+%28-3-i%2Asqrt%2851%29%29%2F%285%29 Reduce.


So the answers are x+=+%28-3%2Bi%2Asqrt%2851%29%29%2F%285%29 or x+=+%28-3-i%2Asqrt%2851%29%29%2F%285%29