SOLUTION: solve -16x2+10x-7=0 =answer is -5+√67)/6,(-5-√67)/6 is this correct?

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Question 475592: solve -16x2+10x-7=0 =answer is -5+√67)/6,(-5-√67)/6 is this correct?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

-16x%5E2%2B10x-7=0 Start with the given equation.


Notice that the quadratic -16x%5E2%2B10x-7 is in the form of Ax%5E2%2BBx%2BC where A=-16, B=10, and C=-7


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%28-16%29%28-7%29+%29%29%2F%282%28-16%29%29 Plug in A=-16, B=10, and C=-7


x+=+%28-10+%2B-+sqrt%28+100-4%28-16%29%28-7%29+%29%29%2F%282%28-16%29%29 Square 10 to get 100.


x+=+%28-10+%2B-+sqrt%28+100-448+%29%29%2F%282%28-16%29%29 Multiply 4%28-16%29%28-7%29 to get 448


x+=+%28-10+%2B-+sqrt%28+-348+%29%29%2F%282%28-16%29%29 Subtract 448 from 100 to get -348


x+=+%28-10+%2B-+sqrt%28+-348+%29%29%2F%28-32%29 Multiply 2 and -16 to get -32.


x+=+%28-10+%2B-+2i%2Asqrt%2887%29%29%2F%28-32%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%28-10%2B2i%2Asqrt%2887%29%29%2F%28-32%29 or x+=+%28-10-2i%2Asqrt%2887%29%29%2F%28-32%29 Break up the expression.


x+=+%285-i%2Asqrt%2887%29%29%2F%2816%29 or x+=+%285%2Bi%2Asqrt%2887%29%29%2F%2816%29 Reduce.


So the solutions are x+=+%285-i%2Asqrt%2887%29%29%2F%2816%29 or x+=+%285%2Bi%2Asqrt%2887%29%29%2F%2816%29