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Simplifying 6x2 + -100x + -200 = 0 Reorder the terms: -200 + -100x + 6x2 = 0 Solving -200 + -100x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-100 + -50x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-100 + -50x + 3x2)' equal to zero and attempt to solve: Simplifying -100 + -50x + 3x2 = 0 Solving -100 + -50x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -33.33333333 + -16.66666667x + x2 = 0 Move the constant term to the right: Add '33.33333333' to each side of the equation. -33.33333333 + -16.66666667x + 33.33333333 + x2 = 0 + 33.33333333 Reorder the terms: -33.33333333 + 33.33333333 + -16.66666667x + x2 = 0 + 33.33333333 Combine like terms: -33.33333333 + 33.33333333 = 0.00000000 0.00000000 + -16.66666667x + x2 = 0 + 33.33333333 -16.66666667x + x2 = 0 + 33.33333333 Combine like terms: 0 + 33.33333333 = 33.33333333 -16.66666667x + x2 = 33.33333333 The x term is -16.66666667x. Take half its coefficient (-8.333333335). Square it (69.44444447) and add it to both sides. Add '69.44444447' to each side of the equation. -16.66666667x + 69.44444447 + x2 = 33.33333333 + 69.44444447 Reorder the terms: 69.44444447 + -16.66666667x + x2 = 33.33333333 + 69.44444447 Combine like terms: 33.33333333 + 69.44444447 = 102.7777778 69.44444447 + -16.66666667x + x2 = 102.7777778 Factor a perfect square on the left side: (x + -8.333333335)(x + -8.333333335) = 102.7777778 Calculate the square root of the right side: 10.137937552 Break this problem into two subproblems by setting (x + -8.333333335) equal to 10.137937552 and -10.137937552.Subproblem 1
x + -8.333333335 = 10.137937552 Simplifying x + -8.333333335 = 10.137937552 Reorder the terms: -8.333333335 + x = 10.137937552 Solving -8.333333335 + x = 10.137937552 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.333333335' to each side of the equation. -8.333333335 + 8.333333335 + x = 10.137937552 + 8.333333335 Combine like terms: -8.333333335 + 8.333333335 = 0.000000000 0.000000000 + x = 10.137937552 + 8.333333335 x = 10.137937552 + 8.333333335 Combine like terms: 10.137937552 + 8.333333335 = 18.471270887 x = 18.471270887 Simplifying x = 18.471270887Subproblem 2
x + -8.333333335 = -10.137937552 Simplifying x + -8.333333335 = -10.137937552 Reorder the terms: -8.333333335 + x = -10.137937552 Solving -8.333333335 + x = -10.137937552 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.333333335' to each side of the equation. -8.333333335 + 8.333333335 + x = -10.137937552 + 8.333333335 Combine like terms: -8.333333335 + 8.333333335 = 0.000000000 0.000000000 + x = -10.137937552 + 8.333333335 x = -10.137937552 + 8.333333335 Combine like terms: -10.137937552 + 8.333333335 = -1.804604217 x = -1.804604217 Simplifying x = -1.804604217Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.471270887, -1.804604217}Solution
x = {18.471270887, -1.804604217}
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