SOLUTION: Solve using the quadratic formula: 4x^2+12x=-3

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Question 46050: Solve using the quadratic formula: 4x^2+12x=-3
Found 2 solutions by venugopalramana, atif.muhammad:
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
Solve using the quadratic formula: 4x^2+12x=-3
4x^2+12x+3=0.....a=4....b=12...c=3
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-12+%2B-+sqrt%28+12%5E2-4%2A4%2A3+%29%29%2F%282%2A4%29+
x+=+%28-12+%2B-+sqrt%28+96+%29%29%2F%288%29+
x+=+%28-12+%2B-+4%2Asqrt%286%29%29%2F%288%29+
x+=+%28-3+%2B-+sqrt%28+6+%29%29%2F%282%29+

Answer by atif.muhammad(135) About Me  (Show Source):
You can put this solution on YOUR website!
Solve using the quadratic formula: 4x^2+12x=-3
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 4x%5E2%2B12x%2B3+=+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=%2812%29%5E2-4%2A4%2A3=96.

Discriminant d=96 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-12%2B-sqrt%28+96+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2812%29%2Bsqrt%28+96+%29%29%2F2%5C4+=+-0.275255128608411
x%5B2%5D+=+%28-%2812%29-sqrt%28+96+%29%29%2F2%5C4+=+-2.72474487139159

Quadratic expression 4x%5E2%2B12x%2B3 can be factored:
4x%5E2%2B12x%2B3+=+4%28x--0.275255128608411%29%2A%28x--2.72474487139159%29
Again, the answer is: -0.275255128608411, -2.72474487139159. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B12%2Ax%2B3+%29