SOLUTION: I have to find the length of an isosceles right triangles legs and the hypotenuse. The hypotenuse is 6 cm longer than either of the legs. I came up with the euqation 2xsquared+(x+6

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Question 112371: I have to find the length of an isosceles right triangles legs and the hypotenuse. The hypotenuse is 6 cm longer than either of the legs. I came up with the euqation 2xsquared+(x+6)squared. However, I can't seem to figure out how to solve that equation to a solution for x.
If you could just point me in the right direction I would be very greatful.
Emily Suspeck
Answer by edjones(8007) (Show Source):
You can put this solution on YOUR website!
Let c=a+6 since a=b
a^2+b^2=c^2
2a^2=(a+6)^2
2a^2=a^2+12a+36
a^2-12a-36=0 subtract the right side from the left side.
a=14.4853...(see below)
c=20.4853...
Check:
2*(14.4853...)^2=20.4853...^2 true
Ed

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=288 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 14.4852813742386, -2.48528137423857. Here's your graph: