SOLUTION: Solve: 5x^2 -4x -33 = 0

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Question 551828: Solve: 5x^2 -4x -33 = 0

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

5x%5E2-4x-33=0 Start with the given equation.


Notice that the quadratic 5x%5E2-4x-33 is in the form of Ax%5E2%2BBx%2BC where A=5, B=-4, and C=-33


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-%28-4%29+%2B-+sqrt%28+%28-4%29%5E2-4%285%29%28-33%29+%29%29%2F%282%285%29%29 Plug in A=5, B=-4, and C=-33


x+=+%284+%2B-+sqrt%28+%28-4%29%5E2-4%285%29%28-33%29+%29%29%2F%282%285%29%29 Negate -4 to get 4.


x+=+%284+%2B-+sqrt%28+16-4%285%29%28-33%29+%29%29%2F%282%285%29%29 Square -4 to get 16.


x+=+%284+%2B-+sqrt%28+16--660+%29%29%2F%282%285%29%29 Multiply 4%285%29%28-33%29 to get -660


x+=+%284+%2B-+sqrt%28+16%2B660+%29%29%2F%282%285%29%29 Rewrite sqrt%2816--660%29 as sqrt%2816%2B660%29


x+=+%284+%2B-+sqrt%28+676+%29%29%2F%282%285%29%29 Add 16 to 660 to get 676


x+=+%284+%2B-+sqrt%28+676+%29%29%2F%2810%29 Multiply 2 and 5 to get 10.


x+=+%284+%2B-+26%29%2F%2810%29 Take the square root of 676 to get 26.


x+=+%284+%2B+26%29%2F%2810%29 or x+=+%284+-+26%29%2F%2810%29 Break up the expression.


x+=+%2830%29%2F%2810%29 or x+=++%28-22%29%2F%2810%29 Combine like terms.


x+=+3 or x+=+-11%2F5 Simplify.


So the solutions are x+=+3 or x+=+-11%2F5