SOLUTION: I need to give the exact solutions to 3 decimal places: x^2 + 2x + 1 = 25 Thank You

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Question 257601: I need to give the exact solutions to 3 decimal places:
x^2 + 2x + 1 = 25
Thank You
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
x^2 + 2x + 1 = 25
x^2 + 2x - 25 = 0
.
Since we can't factor, we must resort to the quadratic equation.
Doing so yields:
x = {4.099, -6.099}
.
Details of quadratic follows:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B2x%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=%282%29%5E2-4%2A1%2A-25=104.

Discriminant d=104 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-2%2B-sqrt%28+104+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%282%29%2Bsqrt%28+104+%29%29%2F2%5C1+=+4.09901951359278
x%5B2%5D+=+%28-%282%29-sqrt%28+104+%29%29%2F2%5C1+=+-6.09901951359278

Quadratic expression 1x%5E2%2B2x%2B-25 can be factored:
1x%5E2%2B2x%2B-25+=+1%28x-4.09901951359278%29%2A%28x--6.09901951359278%29
Again, the answer is: 4.09901951359278, -6.09901951359278. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B2%2Ax%2B-25+%29