SOLUTION: x^2+2x-6=0 Solutions; 1.65 and -3.65 i need the steps between the problem and the solution to help my daughter with her homework please. jhp

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Question 270445: x^2+2x-6=0 Solutions; 1.65 and -3.65
i need the steps between the problem and the solution to help my daughter with her homework please.
jhp
Found 2 solutions by papugai, Alan3354:
Answer by papugai(18) About Me  (Show Source):
You can put this solution on YOUR website!
The given equation is y=x^2 + 2x - 6
Use the quadratic formula: x: x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
The quadratic equation is in the form ax%5E2+%2B+bx+%2B+c+=+y
Sub the values of a, b, and c into the quadratic formula and solve. Notice that there are two solutions because there is a plus or minus before the square root. So in the end, the two answers are
x=1/2[-2+sqrt(28)]
and
x=1/2[-2-sqrt(28)]
When this is solved using the calculator, the answer will be as given in decimal form.
Please comment on how useful this was
Good luck

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
x^2+2x-6=0
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Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B2x%2B-6+=+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-6=28.

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

x%5B1%5D+=+%28-%282%29%2Bsqrt%28+28+%29%29%2F2%5C1+=+1.64575131106459
x%5B2%5D+=+%28-%282%29-sqrt%28+28+%29%29%2F2%5C1+=+-3.64575131106459

Quadratic expression 1x%5E2%2B2x%2B-6 can be factored:
1x%5E2%2B2x%2B-6+=+%28x-1.64575131106459%29%2A%28x--3.64575131106459%29
Again, the answer is: 1.64575131106459, -3.64575131106459. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B2%2Ax%2B-6+%29

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It's -1 ± sqrt(7)