SOLUTION: Please help me solve: {{{ sqrt(5x+1) = x-4 }}}

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Please help me solve: {{{ sqrt(5x+1) = x-4 }}}      Log On


   

Question 155522: Please help me solve: +sqrt%285x%2B1%29+=+x-4+
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x:
sqrt%285x%2B1%29+=+x-4 Square both sides of the equation.
5x%2B1+=+x%5E2-8x%2B16 Subtract 5x from both sides.
1+=+x%5E2-13x%2B16 Subtract 1 from both sides.
x%5E2-13x%2B15+=+0 This is not factorable so use the quadratic formula:x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a Here, a = 1, b = -13, and c = 15, so make the appropriate substitutions:
x+=+%28-%28-13%29%2B-sqrt%28%28-13%29%5E2-4%281%29%2815%29%29%29%2F2%281%29 Simplify.
x+=+%2813%2B-sqrt%28169-60%29%29%2F2
x+=+%2813%2B-sqrt%28109%29%29%2F2
x+=+%2813%2Bsqrt%28109%29%29%2F2 or x+=+%2813-sqrt%28109%29%29%2F2