6x^2+50x-200=0

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Solution for 6x^2+50x-200=0 equation:


Simplifying
6x2 + 50x + -200 = 0

Reorder the terms:
-200 + 50x + 6x2 = 0

Solving
-200 + 50x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-100 + 25x + 3x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-100 + 25x + 3x2)' equal to zero and attempt to solve: Simplifying -100 + 25x + 3x2 = 0 Solving -100 + 25x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -33.33333333 + 8.333333333x + x2 = 0 Move the constant term to the right: Add '33.33333333' to each side of the equation. -33.33333333 + 8.333333333x + 33.33333333 + x2 = 0 + 33.33333333 Reorder the terms: -33.33333333 + 33.33333333 + 8.333333333x + x2 = 0 + 33.33333333 Combine like terms: -33.33333333 + 33.33333333 = 0.00000000 0.00000000 + 8.333333333x + x2 = 0 + 33.33333333 8.333333333x + x2 = 0 + 33.33333333 Combine like terms: 0 + 33.33333333 = 33.33333333 8.333333333x + x2 = 33.33333333 The x term is 8.333333333x. Take half its coefficient (4.166666667). Square it (17.36111111) and add it to both sides. Add '17.36111111' to each side of the equation. 8.333333333x + 17.36111111 + x2 = 33.33333333 + 17.36111111 Reorder the terms: 17.36111111 + 8.333333333x + x2 = 33.33333333 + 17.36111111 Combine like terms: 33.33333333 + 17.36111111 = 50.69444444 17.36111111 + 8.333333333x + x2 = 50.69444444 Factor a perfect square on the left side: (x + 4.166666667)(x + 4.166666667) = 50.69444444 Calculate the square root of the right side: 7.120003121 Break this problem into two subproblems by setting (x + 4.166666667) equal to 7.120003121 and -7.120003121.

Subproblem 1

x + 4.166666667 = 7.120003121 Simplifying x + 4.166666667 = 7.120003121 Reorder the terms: 4.166666667 + x = 7.120003121 Solving 4.166666667 + x = 7.120003121 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.166666667' to each side of the equation. 4.166666667 + -4.166666667 + x = 7.120003121 + -4.166666667 Combine like terms: 4.166666667 + -4.166666667 = 0.000000000 0.000000000 + x = 7.120003121 + -4.166666667 x = 7.120003121 + -4.166666667 Combine like terms: 7.120003121 + -4.166666667 = 2.953336454 x = 2.953336454 Simplifying x = 2.953336454

Subproblem 2

x + 4.166666667 = -7.120003121 Simplifying x + 4.166666667 = -7.120003121 Reorder the terms: 4.166666667 + x = -7.120003121 Solving 4.166666667 + x = -7.120003121 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.166666667' to each side of the equation. 4.166666667 + -4.166666667 + x = -7.120003121 + -4.166666667 Combine like terms: 4.166666667 + -4.166666667 = 0.000000000 0.000000000 + x = -7.120003121 + -4.166666667 x = -7.120003121 + -4.166666667 Combine like terms: -7.120003121 + -4.166666667 = -11.286669788 x = -11.286669788 Simplifying x = -11.286669788

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.953336454, -11.286669788}

Solution

x = {2.953336454, -11.286669788}

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