SOLUTION: x^2 -10x-22=0

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Question 299444: x^2 -10x-22=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2-10x-22=0 Start with the given equation.


Notice that the quadratic x%5E2-10x-22 is in the form of Ax%5E2%2BBx%2BC where A=1, B=-10, and C=-22


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-%28-10%29+%2B-+sqrt%28+%28-10%29%5E2-4%281%29%28-22%29+%29%29%2F%282%281%29%29 Plug in A=1, B=-10, and C=-22


x+=+%2810+%2B-+sqrt%28+%28-10%29%5E2-4%281%29%28-22%29+%29%29%2F%282%281%29%29 Negate -10 to get 10.


x+=+%2810+%2B-+sqrt%28+100-4%281%29%28-22%29+%29%29%2F%282%281%29%29 Square -10 to get 100.


x+=+%2810+%2B-+sqrt%28+100--88+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-22%29 to get -88


x+=+%2810+%2B-+sqrt%28+100%2B88+%29%29%2F%282%281%29%29 Rewrite sqrt%28100--88%29 as sqrt%28100%2B88%29


x+=+%2810+%2B-+sqrt%28+188+%29%29%2F%282%281%29%29 Add 100 to 88 to get 188


x+=+%2810+%2B-+sqrt%28+188+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%2810+%2B-+2%2Asqrt%2847%29%29%2F%282%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%2810%29%2F%282%29+%2B-+%282%2Asqrt%2847%29%29%2F%282%29 Break up the fraction.


x+=+5+%2B-+sqrt%2847%29 Reduce.


x+=+5%2Bsqrt%2847%29 or x+=+5-sqrt%2847%29 Break up the expression.


So the solutions are x+=+5%2Bsqrt%2847%29 or x+=+5-sqrt%2847%29