SOLUTION: x^2 + 8x -4 = 0

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Question 197756: x^2 + 8x -4 = 0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2%2B8x-4=0 Start with the given equation.


Notice we have a quadratic in the form of Ax%5E2%2BBx%2BC where A=1, B=8, and C=-4


Let's use the quadratic formula to solve for "x":


x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


x+=+%28-%288%29+%2B-+sqrt%28+%288%29%5E2-4%281%29%28-4%29+%29%29%2F%282%281%29%29 Plug in A=1, B=8, and C=-4


x+=+%28-8+%2B-+sqrt%28+64-4%281%29%28-4%29+%29%29%2F%282%281%29%29 Square 8 to get 64.


x+=+%28-8+%2B-+sqrt%28+64--16+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-4%29 to get -16


x+=+%28-8+%2B-+sqrt%28+64%2B16+%29%29%2F%282%281%29%29 Rewrite sqrt%2864--16%29 as sqrt%2864%2B16%29


x+=+%28-8+%2B-+sqrt%28+80+%29%29%2F%282%281%29%29 Add 64 to 16 to get 80


x+=+%28-8+%2B-+sqrt%28+80+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%28-8+%2B-+4%2Asqrt%285%29%29%2F%282%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%28-8%29%2F%282%29+%2B-+%284%2Asqrt%285%29%29%2F%282%29 Break up the fraction.


x+=+-4+%2B-+2%2Asqrt%285%29 Reduce.


x+=+-4%2B2%2Asqrt%285%29 or x+=+-4-2%2Asqrt%285%29 Break up the expression.


So the solutions are x+=+-4%2B2%2Asqrt%285%29 or x+=+-4-2%2Asqrt%285%29


which approximate to x=0.472 or x=-8.472