SOLUTION: Solve 2x ( x + 3 ) = x + 25

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Question 167807: Solve 2x ( x + 3 ) = x + 25
Answer by KnightOwlTutor(293) About Me  (Show Source):
You can put this solution on YOUR website!
Use the distributive property to multiply the first part of the equation.
2x^2+6x=x+25
subtract x from both sides
2x^2+5x=25
Subtract 25 from both sides
2x^2+5x-25=0
this is a quadratic equation
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B5x%2B-25+=+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=%285%29%5E2-4%2A2%2A-25=225.

Discriminant d=225 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-5%2B-sqrt%28+225+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%285%29%2Bsqrt%28+225+%29%29%2F2%5C2+=+2.5
x%5B2%5D+=+%28-%285%29-sqrt%28+225+%29%29%2F2%5C2+=+-5

Quadratic expression 2x%5E2%2B5x%2B-25 can be factored:
2x%5E2%2B5x%2B-25+=+2%28x-2.5%29%2A%28x--5%29
Again, the answer is: 2.5, -5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B5%2Ax%2B-25+%29