SOLUTION: Solve : 3(x+2) + 4(x-1) = 7(x+2)(x-1)

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Question 118394: Solve : 3(x+2) + 4(x-1) = 7(x+2)(x-1)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
3%28x%2B2%29+%2B+4%28x-1%29+=+7%28x%2B2%29%28x-1%29 Start with the given equation


3%28x%2B2%29+%2B+4%28x-1%29+=+7%28x%5E2%2Bx-2%29 Foil


3x%2B6+%2B+4x-4+=+7x%5E2%2B7x-14 Distribute



3x%2B6+%2B+4x-4+-+7x%5E2-7x%2B14=0 Get all terms to the left side


-7x%5E2%2B16=0 Combine like terms



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 -7%2Ax%5E2%2B16=0 (note: since the polynomial does not have an "x" term, the 2nd coefficient is zero. In other words, b=0. So that means the polynomial really looks like -7%2Ax%5E2%2B0%2Ax%2B16=0 notice a=-7, b=0, and c=16)




x+=+%280+%2B-+sqrt%28+%280%29%5E2-4%2A-7%2A16+%29%29%2F%282%2A-7%29 Plug in a=-7, b=0, and c=16



x+=+%280+%2B-+sqrt%28+0-4%2A-7%2A16+%29%29%2F%282%2A-7%29 Square 0 to get 0



x+=+%280+%2B-+sqrt%28+0%2B448+%29%29%2F%282%2A-7%29 Multiply -4%2A16%2A-7 to get 448



x+=+%280+%2B-+sqrt%28+448+%29%29%2F%282%2A-7%29 Combine like terms in the radicand (everything under the square root)



x+=+%28-0+%2B-+8%2Asqrt%287%29%29%2F%282%2A-7%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)



x+=+%28-0+%2B-+8%2Asqrt%287%29%29%2F-14 Multiply 2 and -7 to get -14

So now the expression breaks down into two parts

x+=+%28-0+%2B+8%2Asqrt%287%29%29%2F-14 or x+=+%28-0+-+8%2Asqrt%287%29%29%2F-14


Now break up the fraction


x=-0%2F-14%2B8%2Asqrt%287%29%2F-14 or x=-0%2F-14-8%2Asqrt%287%29%2F-14


Simplify


x=0-4%2Asqrt%287%29%2F7 or x=0%2B4%2Asqrt%287%29%2F7


So these expressions approximate to

x=-1.51185789203691 or x=1.51185789203691


So our solutions are:
x=-1.51185789203691 or x=1.51185789203691

Notice when we graph -7%2Ax%5E2%2B16, we get:



when we use the root finder feature on a calculator, we find that x=-1.51185789203691 and x=1.51185789203691.So this verifies our answer