Question 1075003
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Your equation is Pythagorean

{{{x^2 + (x-7)^2}}} = {{{(x+2)^2}}}.


Simplify and solve for x:

{{{x^2 + x^2 - 14x + 49}}} = {{{x^2 + 4x + 4}}},

{{{x^2 - 18x + 45}}} = 0.


Factor left side:

(x-3)*(x-15) = 0.


The root x = 15 is appropriate.
The root x = 3 is EXTRANEOUS solution, since x-7 is negative in this case.

The sides of the triangle are 15, x-7 = 8  and  x+2 = 17.


<U>Answer</U>. The sides are 8, 15 and 17.


<U>Check</U>.  {{{8^2 + 15^2}}} = {{{289}}} = {{{17^2}}}.  Correct !
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