SOLUTION: solve by completing the square. 3x^2+12x-9=0

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Question 170236: solve by completing the square. 3x^2+12x-9=0
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
solve by completing the square. 3x^2+12x-9=0
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3x^2+12x-9=0
Divide by 3
x^2 + 4x - 3 = 0
x^2 + 4x = 3
(x+2)^2 = x^2+4x+4, so add 4
x^2 + 4x + 4 = 3+4
(x+2)^2 = 7
x+2 = +sqrt(7)
x+2 = -sqrt(7)
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x = -2+sqrt(7)
x = -2-sqrt(7)
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Just for grins:
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B4x%2B-3+=+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=%284%29%5E2-4%2A1%2A-3=28.

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

x%5B1%5D+=+%28-%284%29%2Bsqrt%28+28+%29%29%2F2%5C1+=+0.645751311064591
x%5B2%5D+=+%28-%284%29-sqrt%28+28+%29%29%2F2%5C1+=+-4.64575131106459

Quadratic expression 1x%5E2%2B4x%2B-3 can be factored:
1x%5E2%2B4x%2B-3+=+%28x-0.645751311064591%29%2A%28x--4.64575131106459%29
Again, the answer is: 0.645751311064591, -4.64575131106459. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B4%2Ax%2B-3+%29