SOLUTION: Solve using the quadratic formula: 1) x^2-2x=15x-10 2) x^2-3x-3=5 Thank you for the help ;)

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Question 179509: Solve using the quadratic formula:
1) x^2-2x=15x-10

2) x^2-3x-3=5

Thank you for the help ;)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
# 1


x%5E2-2x=15x-10 Start with the given equation.


x%5E2-2x-15x%2B10=0 Get all terms to the left side.


x%5E2-17x%2B10=0 Combine like terms.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=1, b=-17, and c=10


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-%28-17%29+%2B-+sqrt%28+%28-17%29%5E2-4%281%29%2810%29+%29%29%2F%282%281%29%29 Plug in a=1, b=-17, and c=10


x+=+%2817+%2B-+sqrt%28+%28-17%29%5E2-4%281%29%2810%29+%29%29%2F%282%281%29%29 Negate -17 to get 17.


x+=+%2817+%2B-+sqrt%28+289-4%281%29%2810%29+%29%29%2F%282%281%29%29 Square -17 to get 289.


x+=+%2817+%2B-+sqrt%28+289-40+%29%29%2F%282%281%29%29 Multiply 4%281%29%2810%29 to get 40


x+=+%2817+%2B-+sqrt%28+249+%29%29%2F%282%281%29%29 Subtract 40 from 289 to get 249


x+=+%2817+%2B-+sqrt%28+249+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%2817%2Bsqrt%28249%29%29%2F%282%29 or x+=+%2817-sqrt%28249%29%29%2F%282%29 Break up the expression.


So the answers are x+=+%2817%2Bsqrt%28249%29%29%2F%282%29 or x+=+%2817-sqrt%28249%29%29%2F%282%29


which approximate to x=16.39 or x=0.61





# 2




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


x%5E2-3x-3-5=0 Subtract 5 from both sides.


x%5E2-3x-8=0 Combine like terms.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=1, b=-3, and c=-8


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-%28-3%29+%2B-+sqrt%28+%28-3%29%5E2-4%281%29%28-8%29+%29%29%2F%282%281%29%29 Plug in a=1, b=-3, and c=-8


x+=+%283+%2B-+sqrt%28+%28-3%29%5E2-4%281%29%28-8%29+%29%29%2F%282%281%29%29 Negate -3 to get 3.


x+=+%283+%2B-+sqrt%28+9-4%281%29%28-8%29+%29%29%2F%282%281%29%29 Square -3 to get 9.


x+=+%283+%2B-+sqrt%28+9--32+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-8%29 to get -32


x+=+%283+%2B-+sqrt%28+9%2B32+%29%29%2F%282%281%29%29 Rewrite sqrt%289--32%29 as sqrt%289%2B32%29


x+=+%283+%2B-+sqrt%28+41+%29%29%2F%282%281%29%29 Add 9 to 32 to get 41


x+=+%283+%2B-+sqrt%28+41+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%283%2Bsqrt%2841%29%29%2F%282%29 or x+=+%283-sqrt%2841%29%29%2F%282%29 Break up the expression.


So the answers are x+=+%283%2Bsqrt%2841%29%29%2F%282%29 or x+=+%283-sqrt%2841%29%29%2F%282%29


which approximate to x=4.702 or x=-1.702