SOLUTION: 4a^2=4a+5

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Question 1049873: 4a^2=4a+5
Answer by srinivas.g(540) About Me  (Show Source):
You can put this solution on YOUR website!
given that
+4a%5E2+=4a%2B5
move 4a+5 to the left
4a%5E2-4a-5+=+0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation aa%5E2%2Bba%2Bc=0 (in our case 4a%5E2%2B-4a%2B-5+=+0) has the following solutons:

a%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=%28-4%29%5E2-4%2A4%2A-5=96.

Discriminant d=96 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--4%2B-sqrt%28+96+%29%29%2F2%5Ca.

a%5B1%5D+=+%28-%28-4%29%2Bsqrt%28+96+%29%29%2F2%5C4+=+1.72474487139159
a%5B2%5D+=+%28-%28-4%29-sqrt%28+96+%29%29%2F2%5C4+=+-0.724744871391589

Quadratic expression 4a%5E2%2B-4a%2B-5 can be factored:
4a%5E2%2B-4a%2B-5+=+4%28a-1.72474487139159%29%2A%28a--0.724744871391589%29
Again, the answer is: 1.72474487139159, -0.724744871391589. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B-4%2Ax%2B-5+%29