SOLUTION: 1/2x^2 + 5x + 25/2 = 0 I do not even know where to begin. I emailed my teacher but have yet to hear back from her.

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Question 704820: 1/2x^2 + 5x + 25/2 = 0
I do not even know where to begin. I emailed my teacher but have yet to hear back from her.
Found 2 solutions by nerdybill, Stitch:
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
1/2x^2 + 5x + 25/2 = 0
multiplying both sides by 2:
x^2 + 10x + 25 = 0
now, you can easily factor the left:
(x+5)(x+5) = 0
x = {-5}

Answer by Stitch(470) About Me  (Show Source):
You can put this solution on YOUR website!
Given: %281%2F2%29%2AX%5E2+%2B+5X+%2B+25%2F2+=+0
You can use the quadratic equation as the equation stands or it may be easier if you multiply everything by 2 to remove the denominators.
2%2A%28%281%2F2%29%2AX%5E2+%2B+5X+%2B+25%2F2%29+=+2%2A%280%29
Simplify
1%2AX%5E2+%2B+10X+%2B+25+=+0
Simplify
X%5E2+%2B+10X+%2B+25+=+0
Now you can quadratic equation.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B10x%2B25+=+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=%2810%29%5E2-4%2A1%2A25=0.

Discriminant d=0 is zero! That means that there is only one solution: x+=+%28-%2810%29%29%2F2%5C1.
Expression can be factored: 1x%5E2%2B10x%2B25+=+1%28x--5%29%2A%28x--5%29

Again, the answer is: -5, -5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B10%2Ax%2B25+%29

X = -5 & -5
It sounds redundant but since X is raised to the second power in the equation, you will have two answers.