SOLUTION: This is solving using the quadratic formula. help please! (x+4)^2=15-2x^2

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Question 762418: This is solving using the quadratic formula. help please!
(x+4)^2=15-2x^2
Answer by Stitch(470) About Me  (Show Source):
You can put this solution on YOUR website!
Given: %28X%2B4%29%5E2+=+15+-+2X%5E2
Start by rewriting the equation.
%28X%2B4%29%2A%28X%2B4%29+=+15+-+2X%5E2
We can now use FOIL on the left hand side of the equation.
ERROR Algebra::Solver::Engine::invoke_solver_noengine: solver not defined for name 'foil'.
Error occurred executing solver 'foil' .

Rewrite the equation.
X%5E2+%2B+8X+%2B+16+=+15+-+2X%5E2
Add 2X%5E2 to both sides.
3X%5E2+%2B+8X+%2B+16+=+15
Subtract 15 from both sides.
3X%5E2+%2B+8X+%2B+1+=+0
Now use the quadratic equation to solve for X.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation aX%5E2%2BbX%2Bc=0 (in our case 3X%5E2%2B8X%2B1+=+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=%288%29%5E2-4%2A3%2A1=52.

Discriminant d=52 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-8%2B-sqrt%28+52+%29%29%2F2%5Ca.

X%5B1%5D+=+%28-%288%29%2Bsqrt%28+52+%29%29%2F2%5C3+=+-0.13148290817867
X%5B2%5D+=+%28-%288%29-sqrt%28+52+%29%29%2F2%5C3+=+-2.535183758488

Quadratic expression 3X%5E2%2B8X%2B1 can be factored:
3X%5E2%2B8X%2B1+=+3%28X--0.13148290817867%29%2A%28X--2.535183758488%29
Again, the answer is: -0.13148290817867, -2.535183758488. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B8%2Ax%2B1+%29