SOLUTION: how do I solve these problems 1. 6x^2+7x=5 2.12+5x-2x^2=0 3.5x^2+16x-12=0

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Question 199645: how do I solve these problems
1. 6x^2+7x=5

2.12+5x-2x^2=0
3.5x^2+16x-12=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
# 1



6x%5E2%2B7x=5 Start with the given equation.


6x%5E2%2B7x-5=0 Subtract 5 from both sides.


Notice we have a quadratic in the form of Ax%5E2%2BBx%2BC where A=6, B=7, and C=-5


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-%287%29+%2B-+sqrt%28+%287%29%5E2-4%286%29%28-5%29+%29%29%2F%282%286%29%29 Plug in A=6, B=7, and C=-5


x+=+%28-7+%2B-+sqrt%28+49-4%286%29%28-5%29+%29%29%2F%282%286%29%29 Square 7 to get 49.


x+=+%28-7+%2B-+sqrt%28+49--120+%29%29%2F%282%286%29%29 Multiply 4%286%29%28-5%29 to get -120


x+=+%28-7+%2B-+sqrt%28+49%2B120+%29%29%2F%282%286%29%29 Rewrite sqrt%2849--120%29 as sqrt%2849%2B120%29


x+=+%28-7+%2B-+sqrt%28+169+%29%29%2F%282%286%29%29 Add 49 to 120 to get 169


x+=+%28-7+%2B-+sqrt%28+169+%29%29%2F%2812%29 Multiply 2 and 6 to get 12.


x+=+%28-7+%2B-+13%29%2F%2812%29 Take the square root of 169 to get 13.


x+=+%28-7+%2B+13%29%2F%2812%29 or x+=+%28-7+-+13%29%2F%2812%29 Break up the expression.


x+=+%286%29%2F%2812%29 or x+=++%28-20%29%2F%2812%29 Combine like terms.


x+=+1%2F2 or x+=+-5%2F3 Simplify.


So the solutions are x+=+1%2F2 or x+=+-5%2F3




# 2

12%2B5x-2x%5E2=0 Start with the given equation.


-2x%5E2%2B5x%2B12=0 Rearrange the terms.


Notice we have a quadratic in the form of Ax%5E2%2BBx%2BC where A=-2, B=5, and C=12


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-%285%29+%2B-+sqrt%28+%285%29%5E2-4%28-2%29%2812%29+%29%29%2F%282%28-2%29%29 Plug in A=-2, B=5, and C=12


x+=+%28-5+%2B-+sqrt%28+25-4%28-2%29%2812%29+%29%29%2F%282%28-2%29%29 Square 5 to get 25.


x+=+%28-5+%2B-+sqrt%28+25--96+%29%29%2F%282%28-2%29%29 Multiply 4%28-2%29%2812%29 to get -96


x+=+%28-5+%2B-+sqrt%28+25%2B96+%29%29%2F%282%28-2%29%29 Rewrite sqrt%2825--96%29 as sqrt%2825%2B96%29


x+=+%28-5+%2B-+sqrt%28+121+%29%29%2F%282%28-2%29%29 Add 25 to 96 to get 121


x+=+%28-5+%2B-+sqrt%28+121+%29%29%2F%28-4%29 Multiply 2 and -2 to get -4.


x+=+%28-5+%2B-+11%29%2F%28-4%29 Take the square root of 121 to get 11.


x+=+%28-5+%2B+11%29%2F%28-4%29 or x+=+%28-5+-+11%29%2F%28-4%29 Break up the expression.


x+=+%286%29%2F%28-4%29 or x+=++%28-16%29%2F%28-4%29 Combine like terms.


x+=+-3%2F2 or x+=+4 Simplify.


So the solutions are x+=+-3%2F2 or x+=+4





# 3




5x%5E2%2B16x-12=0 Start with the given equation.


Notice we have a quadratic in the form of Ax%5E2%2BBx%2BC where A=5, B=16, and C=-12


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-%2816%29+%2B-+sqrt%28+%2816%29%5E2-4%285%29%28-12%29+%29%29%2F%282%285%29%29 Plug in A=5, B=16, and C=-12


x+=+%28-16+%2B-+sqrt%28+256-4%285%29%28-12%29+%29%29%2F%282%285%29%29 Square 16 to get 256.


x+=+%28-16+%2B-+sqrt%28+256--240+%29%29%2F%282%285%29%29 Multiply 4%285%29%28-12%29 to get -240


x+=+%28-16+%2B-+sqrt%28+256%2B240+%29%29%2F%282%285%29%29 Rewrite sqrt%28256--240%29 as sqrt%28256%2B240%29


x+=+%28-16+%2B-+sqrt%28+496+%29%29%2F%282%285%29%29 Add 256 to 240 to get 496


x+=+%28-16+%2B-+sqrt%28+496+%29%29%2F%2810%29 Multiply 2 and 5 to get 10.


x+=+%28-16+%2B-+4%2Asqrt%2831%29%29%2F%2810%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%28-16%2B4%2Asqrt%2831%29%29%2F%2810%29 or x+=+%28-16-4%2Asqrt%2831%29%29%2F%2810%29 Break up the expression.


x+=+%28-8%2B2%2Asqrt%2831%29%29%2F%285%29 or x+=+%28-8-2%2Asqrt%2831%29%29%2F%285%29 Reduce.


So the solutions are x+=+%28-8%2B2%2Asqrt%2831%29%29%2F%285%29 or x+=+%28-8-2%2Asqrt%2831%29%29%2F%285%29


which approximate to x=0.627 or x=-3.827