SOLUTION: Solve the equation for x: (7x+1)^2+(15x+2)^2=(17x+1)^2 My answer: (7x)^2+2*7x*1+1^2+(15x)^2+2*15x*2+2^2=(17x)^2+2*17x*1+1^2 49x^2+14x+1+225x^2+60x+4=

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Solve the equation for x: (7x+1)^2+(15x+2)^2=(17x+1)^2 My answer: (7x)^2+2*7x*1+1^2+(15x)^2+2*15x*2+2^2=(17x)^2+2*17x*1+1^2 49x^2+14x+1+225x^2+60x+4=      Log On


   

Question 785546: Solve the equation for x: (7x+1)^2+(15x+2)^2=(17x+1)^2
My answer: (7x)^2+2*7x*1+1^2+(15x)^2+2*15x*2+2^2=(17x)^2+2*17x*1+1^2

49x^2+14x+1+225x^2+60x+4=289x^2+34x+1=
274x^2+74x+5=289x^2+34x+1

74x+5=15x^2+34x+1

40x+5=15x^2+1
40x=15x^2-4
x=15x^2-4/40
Austrian Math 8th grade. I can't seem to find the answer. Thank you.
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
7x+1)^2+(15x+2)^2=(17x+1)^2
My answer: (7x)^2+2*7x*1+1^2+(15x)^2+2*15x*2+2^2=(17x)^2+2*17x*1+1^2

49x^2+14x+1+225x^2+60x+4=289x^2+34x+1=
274x^2+74x+5=289x^2+34x+1

74x+5=15x^2+34x+1

40x+5=15x^2+1
40x=15x^2-4
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15x%5E2+-+40x+-+4+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 15x%5E2%2B-40x%2B-4+=+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=%28-40%29%5E2-4%2A15%2A-4=1840.

Discriminant d=1840 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--40%2B-sqrt%28+1840+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-40%29%2Bsqrt%28+1840+%29%29%2F2%5C15+=+2.76317403930181
x%5B2%5D+=+%28-%28-40%29-sqrt%28+1840+%29%29%2F2%5C15+=+-0.0965073726351477

Quadratic expression 15x%5E2%2B-40x%2B-4 can be factored:
15x%5E2%2B-40x%2B-4+=+%28x-2.76317403930181%29%2A%28x--0.0965073726351477%29
Again, the answer is: 2.76317403930181, -0.0965073726351477. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+15%2Ax%5E2%2B-40%2Ax%2B-4+%29

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x+=+4%2F3+%2B+2sqrt%28115%29%2F15
x+=+4%2F3+-+2sqrt%28115%29%2F15


x=15x^2-4/40