SOLUTION: Use the quadratic formula to find the exact solutions. x2 - 14x + 74 = 0

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Question 538092: Use the quadratic formula to find the exact solutions.
x2 - 14x + 74 = 0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2-14x%2B74=0 Start with the given equation.


Notice that the quadratic x%5E2-14x%2B74 is in the form of Ax%5E2%2BBx%2BC where A=1, B=-14, and C=74


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-%28-14%29+%2B-+sqrt%28+%28-14%29%5E2-4%281%29%2874%29+%29%29%2F%282%281%29%29 Plug in A=1, B=-14, and C=74


x+=+%2814+%2B-+sqrt%28+%28-14%29%5E2-4%281%29%2874%29+%29%29%2F%282%281%29%29 Negate -14 to get 14.


x+=+%2814+%2B-+sqrt%28+196-4%281%29%2874%29+%29%29%2F%282%281%29%29 Square -14 to get 196.


x+=+%2814+%2B-+sqrt%28+196-296+%29%29%2F%282%281%29%29 Multiply 4%281%29%2874%29 to get 296


x+=+%2814+%2B-+sqrt%28+-100+%29%29%2F%282%281%29%29 Subtract 296 from 196 to get -100


x+=+%2814+%2B-+sqrt%28+-100+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%2814+%2B-+10%2Ai%29%2F%282%29 Take the square root of -100 to get 10%2Ai.


x+=+%2814+%2B+10%2Ai%29%2F%282%29 or x+=+%2814+-+10%2Ai%29%2F%282%29 Break up the expression.


x+=+%2814%29%2F%282%29+%2B+%2810%2Ai%29%2F%282%29 or x+=++%2814%29%2F%282%29+-+%2810%2Ai%29%2F%282%29 Break up the fraction for each case.


x+=+7%2B5%2Ai or x+=++7-5%2Ai Reduce.


x+=+7%2B5%2Ai or x+=+7-5%2Ai Simplify.


So the solutions are x+=+7%2B5%2Ai or x+=+7-5%2Ai


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