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Simplifying 12x2 + -12x + -100 = 3000 Reorder the terms: -100 + -12x + 12x2 = 3000 Solving -100 + -12x + 12x2 = 3000 Solving for variable 'x'. Reorder the terms: -100 + -3000 + -12x + 12x2 = 3000 + -3000 Combine like terms: -100 + -3000 = -3100 -3100 + -12x + 12x2 = 3000 + -3000 Combine like terms: 3000 + -3000 = 0 -3100 + -12x + 12x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-775 + -3x + 3x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-775 + -3x + 3x2)' equal to zero and attempt to solve: Simplifying -775 + -3x + 3x2 = 0 Solving -775 + -3x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -258.3333333 + -1x + x2 = 0 Move the constant term to the right: Add '258.3333333' to each side of the equation. -258.3333333 + -1x + 258.3333333 + x2 = 0 + 258.3333333 Reorder the terms: -258.3333333 + 258.3333333 + -1x + x2 = 0 + 258.3333333 Combine like terms: -258.3333333 + 258.3333333 = 0.0000000 0.0000000 + -1x + x2 = 0 + 258.3333333 -1x + x2 = 0 + 258.3333333 Combine like terms: 0 + 258.3333333 = 258.3333333 -1x + x2 = 258.3333333 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 258.3333333 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 258.3333333 + 0.25 Combine like terms: 258.3333333 + 0.25 = 258.5833333 0.25 + -1x + x2 = 258.5833333 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 258.5833333 Calculate the square root of the right side: 16.080526524 Break this problem into two subproblems by setting (x + -0.5) equal to 16.080526524 and -16.080526524.Subproblem 1
x + -0.5 = 16.080526524 Simplifying x + -0.5 = 16.080526524 Reorder the terms: -0.5 + x = 16.080526524 Solving -0.5 + x = 16.080526524 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 16.080526524 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 16.080526524 + 0.5 x = 16.080526524 + 0.5 Combine like terms: 16.080526524 + 0.5 = 16.580526524 x = 16.580526524 Simplifying x = 16.580526524Subproblem 2
x + -0.5 = -16.080526524 Simplifying x + -0.5 = -16.080526524 Reorder the terms: -0.5 + x = -16.080526524 Solving -0.5 + x = -16.080526524 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -16.080526524 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -16.080526524 + 0.5 x = -16.080526524 + 0.5 Combine like terms: -16.080526524 + 0.5 = -15.580526524 x = -15.580526524 Simplifying x = -15.580526524Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.580526524, -15.580526524}Solution
x = {16.580526524, -15.580526524}
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