SOLUTION: Could some one please help me solve this equation. {{{6x^2+7x=7}}}

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Question 103981: Could some one please help me solve this equation.
6x%5E2%2B7x=7
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
6x%5E2%2B7x=7 Start with the given equation


6x%5E2%2B7x-7=0 Subtract 7 from both sides


Let's use the quadratic formula to solve for x:


Starting with the general quadratic

ax%5E2%2Bbx%2Bc=0

the general solution using the quadratic equation is:

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29



So lets solve 6%2Ax%5E2%2B7%2Ax-7=0 ( notice a=6, b=7, and c=-7)




x+=+%28-7+%2B-+sqrt%28+%287%29%5E2-4%2A6%2A-7+%29%29%2F%282%2A6%29 Plug in a=6, b=7, and c=-7



x+=+%28-7+%2B-+sqrt%28+49-4%2A6%2A-7+%29%29%2F%282%2A6%29 Square 7 to get 49



x+=+%28-7+%2B-+sqrt%28+49%2B168+%29%29%2F%282%2A6%29 Multiply -4%2A-7%2A6 to get 168



x+=+%28-7+%2B-+sqrt%28+217+%29%29%2F%282%2A6%29 Combine like terms in the radicand (everything under the square root)



x+=+%28-7+%2B-+sqrt%28217%29%29%2F%282%2A6%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)



x+=+%28-7+%2B-+sqrt%28217%29%29%2F12 Multiply 2 and 6 to get 12

So now the expression breaks down into two parts

x+=+%28-7+%2B+sqrt%28217%29%29%2F12 or x+=+%28-7+-+sqrt%28217%29%29%2F12


Now break up the fraction


x=-7%2F12%2Bsqrt%28217%29%2F12 or x=-7%2F12-sqrt%28217%29%2F12


Simplify


x=-7+%2F+12%2Bsqrt%28217%29%2F12 or x=-7+%2F+12-sqrt%28217%29%2F12


So these expressions approximate to

x=0.64424332188802 or x=-1.81090998855469


So our solutions are:
x=0.64424332188802 or x=-1.81090998855469

Notice when we graph 6%2Ax%5E2%2B7%2Ax-7, we get:



when we use the root finder feature on a calculator, we find that x=0.64424332188802 and x=-1.81090998855469.So this verifies our answer