SOLUTION: Solve: 2x+2=5 square root of x

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Question 170700: Solve: 2x+2=5 square root of x
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
2x%2B2=5sqrt%28x%29lets square both sides to get rid of the radical%285sqrt%28x%29%29%5E2=25x%29
:
%282x%2B2%29%5E2=25x
:
4x%5E2%2B8x%2B4=25x
:
4x%5E2-17x%2B4=0
answer:---system%28x=4%2Cx=.25%29
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 4x%5E2%2B-17x%2B4+=+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=%28-17%29%5E2-4%2A4%2A4=225.

Discriminant d=225 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--17%2B-sqrt%28+225+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-17%29%2Bsqrt%28+225+%29%29%2F2%5C4+=+4
x%5B2%5D+=+%28-%28-17%29-sqrt%28+225+%29%29%2F2%5C4+=+0.25

Quadratic expression 4x%5E2%2B-17x%2B4 can be factored:
4x%5E2%2B-17x%2B4+=+4%28x-4%29%2A%28x-0.25%29
Again, the answer is: 4, 0.25. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B-17%2Ax%2B4+%29