SOLUTION: x^2-6x-28=0

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Question 570939: x^2-6x-28=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2-6x-28=0 Start with the given equation.


Notice that the quadratic x%5E2-6x-28 is in the form of Ax%5E2%2BBx%2BC where A=1, B=-6, and C=-28


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-%28-6%29+%2B-+sqrt%28+%28-6%29%5E2-4%281%29%28-28%29+%29%29%2F%282%281%29%29 Plug in A=1, B=-6, and C=-28


x+=+%286+%2B-+sqrt%28+%28-6%29%5E2-4%281%29%28-28%29+%29%29%2F%282%281%29%29 Negate -6 to get 6.


x+=+%286+%2B-+sqrt%28+36-4%281%29%28-28%29+%29%29%2F%282%281%29%29 Square -6 to get 36.


x+=+%286+%2B-+sqrt%28+36--112+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-28%29 to get -112


x+=+%286+%2B-+sqrt%28+36%2B112+%29%29%2F%282%281%29%29 Rewrite sqrt%2836--112%29 as sqrt%2836%2B112%29


x+=+%286+%2B-+sqrt%28+148+%29%29%2F%282%281%29%29 Add 36 to 112 to get 148


x+=+%286+%2B-+sqrt%28+148+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%286+%2B-+2%2Asqrt%2837%29%29%2F%282%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%286%29%2F%282%29+%2B-+%282%2Asqrt%2837%29%29%2F%282%29 Break up the fraction.


x+=+3+%2B-+sqrt%2837%29 Reduce.


x+=+3%2Bsqrt%2837%29 or x+=+3-sqrt%2837%29 Break up the expression.


So the solutions are x+=+3%2Bsqrt%2837%29 or x+=+3-sqrt%2837%29