SOLUTION: solve for x: 3x^2+4x-9=0

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Question 123070: solve for x: 3x^2+4x-9=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
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 3%2Ax%5E2%2B4%2Ax-9=0 ( notice a=3, b=4, and c=-9)




x+=+%28-4+%2B-+sqrt%28+%284%29%5E2-4%2A3%2A-9+%29%29%2F%282%2A3%29 Plug in a=3, b=4, and c=-9



x+=+%28-4+%2B-+sqrt%28+16-4%2A3%2A-9+%29%29%2F%282%2A3%29 Square 4 to get 16



x+=+%28-4+%2B-+sqrt%28+16%2B108+%29%29%2F%282%2A3%29 Multiply -4%2A-9%2A3 to get 108



x+=+%28-4+%2B-+sqrt%28+124+%29%29%2F%282%2A3%29 Combine like terms in the radicand (everything under the square root)



x+=+%28-4+%2B-+2%2Asqrt%2831%29%29%2F%282%2A3%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)



x+=+%28-4+%2B-+2%2Asqrt%2831%29%29%2F6 Multiply 2 and 3 to get 6

So now the expression breaks down into two parts

x+=+%28-4+%2B+2%2Asqrt%2831%29%29%2F6 or x+=+%28-4+-+2%2Asqrt%2831%29%29%2F6


Now break up the fraction


x=-4%2F6%2B2%2Asqrt%2831%29%2F6 or x=-4%2F6-2%2Asqrt%2831%29%2F6


Simplify


x=-2+%2F+3%2Bsqrt%2831%29%2F3 or x=-2+%2F+3-sqrt%2831%29%2F3


So these expressions approximate to

x=1.18925478761001 or x=-2.52258812094334


So our solutions are:
x=1.18925478761001 or x=-2.52258812094334

Notice when we graph 3%2Ax%5E2%2B4%2Ax-9, we get:



when we use the root finder feature on a calculator, we find that x=1.18925478761001 and x=-2.52258812094334.So this verifies our answer