SOLUTION: Solve using the quadratic formula: x^2 – 3x = 7x – 2

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Question 147240: Solve using the quadratic formula:
x^2 – 3x = 7x – 2

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

x%5E2-3x=7x-2 Start with the given equation.


x%5E2-3x-7x%2B2=0 Get all terms to the left side.


x%5E2-10x%2B2=0 Combine like terms.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=1, b=-10, and c=2


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-%28-10%29+%2B-+sqrt%28+%28-10%29%5E2-4%281%29%282%29+%29%29%2F%282%281%29%29 Plug in a=1, b=-10, and c=2


x+=+%2810+%2B-+sqrt%28+%28-10%29%5E2-4%281%29%282%29+%29%29%2F%282%281%29%29 Negate -10 to get 10.


x+=+%2810+%2B-+sqrt%28+100-4%281%29%282%29+%29%29%2F%282%281%29%29 Square -10 to get 100.


x+=+%2810+%2B-+sqrt%28+100-8+%29%29%2F%282%281%29%29 Multiply 4%281%29%282%29 to get 8


x+=+%2810+%2B-+sqrt%28+92+%29%29%2F%282%281%29%29 Subtract 8 from 100 to get 92


x+=+%2810+%2B-+sqrt%28+92+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%2810+%2B-+2%2Asqrt%2823%29%29%2F%282%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%2810%29%2F%282%29+%2B-+%282%2Asqrt%2823%29%29%2F%282%29 Break up the fraction.


x+=+5+%2B-+sqrt%2823%29 Reduce.


x+=+5%2Bsqrt%2823%29 or x+=+5-sqrt%2823%29 Break up the expression.


So our answers are x+=+5%2Bsqrt%2823%29 or x+=+5-sqrt%2823%29


which approximate to x=9.796 or x=0.204