SOLUTION: How do you solve these? 2x^2-12x = -14 and -4r^2+21r = r + 13

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Question 183988This question is from textbook Mcdougal Littell Algebra 2
: How do you solve these?
2x^2-12x = -14 and -4r^2+21r = r + 13This question is from textbook Mcdougal Littell Algebra 2

Answer by jim_thompson5910(28708) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do the first one to get you started

# 1



2x%5E2-12x=-14 Start with the given equation.


2x%5E2-12x%2B14=0 Add 14 to both sides.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=2, b=-12, and c=14


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-%28-12%29+%2B-+sqrt%28+%28-12%29%5E2-4%282%29%2814%29+%29%29%2F%282%282%29%29 Plug in a=2, b=-12, and c=14


x+=+%2812+%2B-+sqrt%28+%28-12%29%5E2-4%282%29%2814%29+%29%29%2F%282%282%29%29 Negate -12 to get 12.


x+=+%2812+%2B-+sqrt%28+144-4%282%29%2814%29+%29%29%2F%282%282%29%29 Square -12 to get 144.


x+=+%2812+%2B-+sqrt%28+144-112+%29%29%2F%282%282%29%29 Multiply 4%282%29%2814%29 to get 112


x+=+%2812+%2B-+sqrt%28+32+%29%29%2F%282%282%29%29 Subtract 112 from 144 to get 32


x+=+%2812+%2B-+sqrt%28+32+%29%29%2F%284%29 Multiply 2 and 2 to get 4.


x+=+%2812+%2B-+4%2Asqrt%282%29%29%2F%284%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%2812%29%2F%284%29+%2B-+%284%2Asqrt%282%29%29%2F%284%29 Break up the fraction.


x+=+3+%2B-+sqrt%282%29 Reduce.


x+=+3%2Bsqrt%282%29 or x+=+3-sqrt%282%29 Break up the expression.


So the solutions are x+=+3%2Bsqrt%282%29 or x+=+3-sqrt%282%29