SOLUTION: Solve by the Quadratic Formula. 3x^2-2x-7=0

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Question 600662: Solve by the Quadratic Formula.
3x^2-2x-7=0




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

3x%5E2-2x-7=0 Start with the given equation.


Notice that the quadratic 3x%5E2-2x-7 is in the form of Ax%5E2%2BBx%2BC where A=3, B=-2, and C=-7


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-%28-2%29+%2B-+sqrt%28+%28-2%29%5E2-4%283%29%28-7%29+%29%29%2F%282%283%29%29 Plug in A=3, B=-2, and C=-7


x+=+%282+%2B-+sqrt%28+%28-2%29%5E2-4%283%29%28-7%29+%29%29%2F%282%283%29%29 Negate -2 to get 2.


x+=+%282+%2B-+sqrt%28+4-4%283%29%28-7%29+%29%29%2F%282%283%29%29 Square -2 to get 4.


x+=+%282+%2B-+sqrt%28+4--84+%29%29%2F%282%283%29%29 Multiply 4%283%29%28-7%29 to get -84


x+=+%282+%2B-+sqrt%28+4%2B84+%29%29%2F%282%283%29%29 Rewrite sqrt%284--84%29 as sqrt%284%2B84%29


x+=+%282+%2B-+sqrt%28+88+%29%29%2F%282%283%29%29 Add 4 to 84 to get 88


x+=+%282+%2B-+sqrt%28+88+%29%29%2F%286%29 Multiply 2 and 3 to get 6.


x+=+%282+%2B-+2%2Asqrt%2822%29%29%2F%286%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%282%2B2%2Asqrt%2822%29%29%2F%286%29 or x+=+%282-2%2Asqrt%2822%29%29%2F%286%29 Break up the expression.


x+=+%281%2Bsqrt%2822%29%29%2F%283%29 or x+=+%281-sqrt%2822%29%29%2F%283%29 Reduce


So the solutions are x+=+%281%2Bsqrt%2822%29%29%2F%283%29 or x+=+%281-sqrt%2822%29%29%2F%283%29