SOLUTION: Hello, using the quadratic formula, can you help me solve 3x^2-12x+11=0?

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Question 264149: Hello, using the quadratic formula, can you help me solve 3x^2-12x+11=0?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

3x%5E2-12x%2B11=0 Start with the given equation.


Notice that the quadratic 3x%5E2-12x%2B11 is in the form of Ax%5E2%2BBx%2BC where A=3, B=-12, and C=11


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-%28-12%29+%2B-+sqrt%28+%28-12%29%5E2-4%283%29%2811%29+%29%29%2F%282%283%29%29 Plug in A=3, B=-12, and C=11


x+=+%2812+%2B-+sqrt%28+%28-12%29%5E2-4%283%29%2811%29+%29%29%2F%282%283%29%29 Negate -12 to get 12.


x+=+%2812+%2B-+sqrt%28+144-4%283%29%2811%29+%29%29%2F%282%283%29%29 Square -12 to get 144.


x+=+%2812+%2B-+sqrt%28+144-132+%29%29%2F%282%283%29%29 Multiply 4%283%29%2811%29 to get 132


x+=+%2812+%2B-+sqrt%28+12+%29%29%2F%282%283%29%29 Subtract 132 from 144 to get 12


x+=+%2812+%2B-+sqrt%28+12+%29%29%2F%286%29 Multiply 2 and 3 to get 6.


x+=+%2812+%2B-+2%2Asqrt%283%29%29%2F%286%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%2812%2B2%2Asqrt%283%29%29%2F%286%29 or x+=+%2812-2%2Asqrt%283%29%29%2F%286%29 Break up the expression.


x+=+%286%2Bsqrt%283%29%29%2F%283%29 or x+=+%286-sqrt%283%29%29%2F%283%29 Reduce.


So the solutions are x+=+%286%2Bsqrt%283%29%29%2F%283%29 or x+=+%286-sqrt%283%29%29%2F%283%29