SOLUTION: solve using the quadratic formula 1) 9x^2+10x-13=0 2) 5y^2-8y=2 Thanks

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Question 585217: solve using the quadratic formula
1) 9x^2+10x-13=0

2) 5y^2-8y=2

Thanks
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
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# 1


9x%5E2%2B10x-13=0 Start with the given equation.


Notice that the quadratic 9x%5E2%2B10x-13 is in the form of Ax%5E2%2BBx%2BC where A=9, B=10, and C=-13


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-%2810%29+%2B-+sqrt%28+%2810%29%5E2-4%289%29%28-13%29+%29%29%2F%282%289%29%29 Plug in A=9, B=10, and C=-13


x+=+%28-10+%2B-+sqrt%28+100-4%289%29%28-13%29+%29%29%2F%282%289%29%29 Square 10 to get 100.


x+=+%28-10+%2B-+sqrt%28+100--468+%29%29%2F%282%289%29%29 Multiply 4%289%29%28-13%29 to get -468


x+=+%28-10+%2B-+sqrt%28+100%2B468+%29%29%2F%282%289%29%29 Rewrite sqrt%28100--468%29 as sqrt%28100%2B468%29


x+=+%28-10+%2B-+sqrt%28+568+%29%29%2F%282%289%29%29 Add 100 to 468 to get 568


x+=+%28-10+%2B-+sqrt%28+568+%29%29%2F%2818%29 Multiply 2 and 9 to get 18.


x+=+%28-10+%2B-+2%2Asqrt%28142%29%29%2F%2818%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%28-10%2B2%2Asqrt%28142%29%29%2F%2818%29 or x+=+%28-10-2%2Asqrt%28142%29%29%2F%2818%29 Break up the expression.


x+=+%28-5%2Bsqrt%28142%29%29%2F%289%29 or x+=+%28-5-sqrt%28142%29%29%2F%289%29 Reduce


So the solutions are x+=+%28-5%2Bsqrt%28142%29%29%2F%289%29 or x+=+%28-5-sqrt%28142%29%29%2F%289%29
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# 2


5y%5E2-8y=2 Start with the given equation.


5y%5E2-8y-2=0 Subtract 2 from both sides.


Notice that the quadratic 5y%5E2-8y-2 is in the form of Ay%5E2%2BBy%2BC where A=5, B=-8, and C=-2


Let's use the quadratic formula to solve for "y":


y+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


y+=+%28-%28-8%29+%2B-+sqrt%28+%28-8%29%5E2-4%285%29%28-2%29+%29%29%2F%282%285%29%29 Plug in A=5, B=-8, and C=-2


y+=+%288+%2B-+sqrt%28+%28-8%29%5E2-4%285%29%28-2%29+%29%29%2F%282%285%29%29 Negate -8 to get 8.


y+=+%288+%2B-+sqrt%28+64-4%285%29%28-2%29+%29%29%2F%282%285%29%29 Square -8 to get 64.


y+=+%288+%2B-+sqrt%28+64--40+%29%29%2F%282%285%29%29 Multiply 4%285%29%28-2%29 to get -40


y+=+%288+%2B-+sqrt%28+64%2B40+%29%29%2F%282%285%29%29 Rewrite sqrt%2864--40%29 as sqrt%2864%2B40%29


y+=+%288+%2B-+sqrt%28+104+%29%29%2F%282%285%29%29 Add 64 to 40 to get 104


y+=+%288+%2B-+sqrt%28+104+%29%29%2F%2810%29 Multiply 2 and 5 to get 10.


y+=+%288+%2B-+2%2Asqrt%2826%29%29%2F%2810%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


y+=+%288%2B2%2Asqrt%2826%29%29%2F%2810%29 or y+=+%288-2%2Asqrt%2826%29%29%2F%2810%29 Break up the expression.


y+=+%284%2Bsqrt%2826%29%29%2F%285%29 or y+=+%284-sqrt%2826%29%29%2F%285%29 Reduce


So the solutions are y+=+%284%2Bsqrt%2826%29%29%2F%285%29 or y+=+%284-sqrt%2826%29%29%2F%285%29

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