SOLUTION: Find the lengths of the sides of the triangles: sides are x and x+1 and the hypotenuse is x+4. So I end up getting x^2 -6x-15= 0 but I don't know how to factor this. What am I doin

Algebra ->  Algebra  -> Pythagorean-theorem -> SOLUTION: Find the lengths of the sides of the triangles: sides are x and x+1 and the hypotenuse is x+4. So I end up getting x^2 -6x-15= 0 but I don't know how to factor this. What am I doin      Log On

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Question 367266: Find the lengths of the sides of the triangles: sides are x and x+1 and the hypotenuse is x+4. So I end up getting x^2 -6x-15= 0 but I don't know how to factor this. What am I doing wrong?
Answer by Alan3354(30959) About Me  (Show Source):
You can put this solution on YOUR website!
Find the lengths of the sides of the triangles: sides are x and x+1 and the hypotenuse is x+4. So I end up getting x^2 -6x-15= 0 but I don't know how to factor this. What am I doing wrong?
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x%5E2+%2B+%28x%2B1%29%5E2+=+%28x%2B4%29%5E2
2x%5E2+%2B+2x+%2B+1+=+x%5E2+%2B+8x+%2B+16
x%5E2+-+6x+-+15+=+0
It doesn't factor
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-6x%2B-15+=+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=%28-6%29%5E2-4%2A1%2A-15=96.

Discriminant d=96 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--6%2B-sqrt%28+96+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-6%29%2Bsqrt%28+96+%29%29%2F2%5C1+=+7.89897948556636
x%5B2%5D+=+%28-%28-6%29-sqrt%28+96+%29%29%2F2%5C1+=+-1.89897948556636

Quadratic expression 1x%5E2%2B-6x%2B-15 can be factored:
1x%5E2%2B-6x%2B-15+=+%28x-7.89897948556636%29%2A%28x--1.89897948556636%29
Again, the answer is: 7.89897948556636, -1.89897948556636. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-6%2Ax%2B-15+%29

Ignore the negative number
x = 3 + 2sqrt(6)