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Simplifying 12x2 + -396x + 3 = 0 Reorder the terms: 3 + -396x + 12x2 = 0 Solving 3 + -396x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(1 + -132x + 4x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(1 + -132x + 4x2)' equal to zero and attempt to solve: Simplifying 1 + -132x + 4x2 = 0 Solving 1 + -132x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.25 + -33x + x2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + -33x + -0.25 + x2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + -33x + x2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + -33x + x2 = 0 + -0.25 -33x + x2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 -33x + x2 = -0.25 The x term is -33x. Take half its coefficient (-16.5). Square it (272.25) and add it to both sides. Add '272.25' to each side of the equation. -33x + 272.25 + x2 = -0.25 + 272.25 Reorder the terms: 272.25 + -33x + x2 = -0.25 + 272.25 Combine like terms: -0.25 + 272.25 = 272 272.25 + -33x + x2 = 272 Factor a perfect square on the left side: (x + -16.5)(x + -16.5) = 272 Calculate the square root of the right side: 16.492422502 Break this problem into two subproblems by setting (x + -16.5) equal to 16.492422502 and -16.492422502.Subproblem 1
x + -16.5 = 16.492422502 Simplifying x + -16.5 = 16.492422502 Reorder the terms: -16.5 + x = 16.492422502 Solving -16.5 + x = 16.492422502 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.5' to each side of the equation. -16.5 + 16.5 + x = 16.492422502 + 16.5 Combine like terms: -16.5 + 16.5 = 0.0 0.0 + x = 16.492422502 + 16.5 x = 16.492422502 + 16.5 Combine like terms: 16.492422502 + 16.5 = 32.992422502 x = 32.992422502 Simplifying x = 32.992422502Subproblem 2
x + -16.5 = -16.492422502 Simplifying x + -16.5 = -16.492422502 Reorder the terms: -16.5 + x = -16.492422502 Solving -16.5 + x = -16.492422502 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.5' to each side of the equation. -16.5 + 16.5 + x = -16.492422502 + 16.5 Combine like terms: -16.5 + 16.5 = 0.0 0.0 + x = -16.492422502 + 16.5 x = -16.492422502 + 16.5 Combine like terms: -16.492422502 + 16.5 = 0.007577498 x = 0.007577498 Simplifying x = 0.007577498Solution
The solution to the problem is based on the solutions from the subproblems. x = {32.992422502, 0.007577498}Solution
x = {32.992422502, 0.007577498}
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