SOLUTION: Find the root of the quadratic equation x^2-8x+15=0

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Question 263181: Find the root of the quadratic equation x^2-8x+15=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2-8x%2B15=0 Start with the given equation.


Notice that the quadratic x%5E2-8x%2B15 is in the form of Ax%5E2%2BBx%2BC where A=1, B=-8, and C=15


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-%28-8%29+%2B-+sqrt%28+%28-8%29%5E2-4%281%29%2815%29+%29%29%2F%282%281%29%29 Plug in A=1, B=-8, and C=15


x+=+%288+%2B-+sqrt%28+%28-8%29%5E2-4%281%29%2815%29+%29%29%2F%282%281%29%29 Negate -8 to get 8.


x+=+%288+%2B-+sqrt%28+64-4%281%29%2815%29+%29%29%2F%282%281%29%29 Square -8 to get 64.


x+=+%288+%2B-+sqrt%28+64-60+%29%29%2F%282%281%29%29 Multiply 4%281%29%2815%29 to get 60


x+=+%288+%2B-+sqrt%28+4+%29%29%2F%282%281%29%29 Subtract 60 from 64 to get 4


x+=+%288+%2B-+sqrt%28+4+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%288+%2B-+2%29%2F%282%29 Take the square root of 4 to get 2.


x+=+%288+%2B+2%29%2F%282%29 or x+=+%288+-+2%29%2F%282%29 Break up the expression.


x+=+%2810%29%2F%282%29 or x+=++%286%29%2F%282%29 Combine like terms.


x+=+5 or x+=+3 Simplify.


So the solutions are x+=+5 or x+=+3