SOLUTION: 33x^2+10x-2=0

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Question 216865: 33x^2+10x-2=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

33x%5E2%2B10x-2=0 Start with the given equation.


Notice that the quadratic 33x%5E2%2B10x-2 is in the form of Ax%5E2%2BBx%2BC where A=33, B=10, and C=-2


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-%2810%29+%2B-+sqrt%28+%2810%29%5E2-4%2833%29%28-2%29+%29%29%2F%282%2833%29%29 Plug in A=33, B=10, and C=-2


x+=+%28-10+%2B-+sqrt%28+100-4%2833%29%28-2%29+%29%29%2F%282%2833%29%29 Square 10 to get 100.


x+=+%28-10+%2B-+sqrt%28+100--264+%29%29%2F%282%2833%29%29 Multiply 4%2833%29%28-2%29 to get -264


x+=+%28-10+%2B-+sqrt%28+100%2B264+%29%29%2F%282%2833%29%29 Rewrite sqrt%28100--264%29 as sqrt%28100%2B264%29


x+=+%28-10+%2B-+sqrt%28+364+%29%29%2F%282%2833%29%29 Add 100 to 264 to get 364


x+=+%28-10+%2B-+sqrt%28+364+%29%29%2F%2866%29 Multiply 2 and 33 to get 66.


x+=+%28-10+%2B-+2%2Asqrt%2891%29%29%2F%2866%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%28-10%2B2%2Asqrt%2891%29%29%2F%2866%29 or x+=+%28-10-2%2Asqrt%2891%29%29%2F%2866%29 Break up the expression.


x+=+%28-5%2Bsqrt%2891%29%29%2F%2833%29 or x+=+%28-5-sqrt%2891%29%29%2F%2833%29 Reduce


So the solutions are x+=+%28-5%2Bsqrt%2891%29%29%2F%2833%29 or x+=+%28-5-sqrt%2891%29%29%2F%2833%29


which approximate to x=0.138 or x=-0.441