SOLUTION: solve using the quadratic formula. 5x^2-3x-3=0

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Question 206761: solve using the quadratic formula. 5x^2-3x-3=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

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


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


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-%28-3%29+%2B-+sqrt%28+%28-3%29%5E2-4%285%29%28-3%29+%29%29%2F%282%285%29%29 Plug in A=5, B=-3, and C=-3


x+=+%283+%2B-+sqrt%28+%28-3%29%5E2-4%285%29%28-3%29+%29%29%2F%282%285%29%29 Negate -3 to get 3.


x+=+%283+%2B-+sqrt%28+9-4%285%29%28-3%29+%29%29%2F%282%285%29%29 Square -3 to get 9.


x+=+%283+%2B-+sqrt%28+9--60+%29%29%2F%282%285%29%29 Multiply 4%285%29%28-3%29 to get -60


x+=+%283+%2B-+sqrt%28+9%2B60+%29%29%2F%282%285%29%29 Rewrite sqrt%289--60%29 as sqrt%289%2B60%29


x+=+%283+%2B-+sqrt%28+69+%29%29%2F%282%285%29%29 Add 9 to 60 to get 69


x+=+%283+%2B-+sqrt%28+69+%29%29%2F%2810%29 Multiply 2 and 5 to get 10.


x+=+%283%2Bsqrt%2869%29%29%2F%2810%29 or x+=+%283-sqrt%2869%29%29%2F%2810%29 Break up the expression.


So the solutions are x+=+%283%2Bsqrt%2869%29%29%2F%2810%29 or x+=+%283-sqrt%2869%29%29%2F%2810%29


which approximate to x=1.131 or x=-0.531