SOLUTION: please help me solve this problem using the quadratic root formula: {{{x^2-x+20=0}}}

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Question 151058: please help me solve this problem using the quadratic root formula: x%5E2-x%2B20=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2-x%2B20=0 Start with the given equation.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=1, b=-1, and c=20


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-%28-1%29+%2B-+sqrt%28+%28-1%29%5E2-4%281%29%2820%29+%29%29%2F%282%281%29%29 Plug in a=1, b=-1, and c=20


x+=+%281+%2B-+sqrt%28+%28-1%29%5E2-4%281%29%2820%29+%29%29%2F%282%281%29%29 Negate -1 to get 1.


x+=+%281+%2B-+sqrt%28+1-4%281%29%2820%29+%29%29%2F%282%281%29%29 Square -1 to get 1.


x+=+%281+%2B-+sqrt%28+1-80+%29%29%2F%282%281%29%29 Multiply 4%281%29%2820%29 to get 80


x+=+%281+%2B-+sqrt%28+-79+%29%29%2F%282%281%29%29 Subtract 80 from 1 to get -79


x+=+%281+%2B-+sqrt%28+-79+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%281+%2B-+i%2Asqrt%2879%29%29%2F%282%29 Simplify the square root


x+=+%281%2Bi%2Asqrt%2879%29%29%2F%282%29 or x+=+%281-i%2Asqrt%2879%29%29%2F%282%29 Break up the expression.


So our answers are x+=+%281%2Bi%2Asqrt%2879%29%29%2F%282%29 or x+=+%281-i%2Asqrt%2879%29%29%2F%282%29


which approximate to x=0.5%2B4.444%2Ai or x=0.5-4.444%2Ai