SOLUTION: I need your help with this: Find the real or imaginary solutions by using the quadratic formula. x square - 12x + 52=0 Thanks

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Question 318038: I need your help with this: Find the real or imaginary solutions by using the quadratic formula. x square - 12x + 52=0

Thanks
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2-12x%2B52=0 Start with the given equation.


Notice that the quadratic x%5E2-12x%2B52 is in the form of Ax%5E2%2BBx%2BC where A=1, B=-12, and C=52


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-%28-12%29+%2B-+sqrt%28+%28-12%29%5E2-4%281%29%2852%29+%29%29%2F%282%281%29%29 Plug in A=1, B=-12, and C=52


x+=+%2812+%2B-+sqrt%28+%28-12%29%5E2-4%281%29%2852%29+%29%29%2F%282%281%29%29 Negate -12 to get 12.


x+=+%2812+%2B-+sqrt%28+144-4%281%29%2852%29+%29%29%2F%282%281%29%29 Square -12 to get 144.


x+=+%2812+%2B-+sqrt%28+144-208+%29%29%2F%282%281%29%29 Multiply 4%281%29%2852%29 to get 208


x+=+%2812+%2B-+sqrt%28+-64+%29%29%2F%282%281%29%29 Subtract 208 from 144 to get -64


x+=+%2812+%2B-+sqrt%28+-64+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%2812+%2B-+8%2Ai%29%2F%282%29 Take the square root of -64 to get 8%2Ai.


x+=+%2812+%2B+8%2Ai%29%2F%282%29 or x+=+%2812+-+8%2Ai%29%2F%282%29 Break up the expression.


x+=+%2812%29%2F%282%29+%2B+%288%2Ai%29%2F%282%29 or x+=++%2812%29%2F%282%29+-+%288%2Ai%29%2F%282%29 Break up the fraction for each case.


x+=+6%2B4%2Ai or x+=++6-4%2Ai Reduce.


So the solutions are x+=+6%2B4%2Ai or x+=+6-4%2Ai