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Simplifying 36x2 + -33x + -18 = 0 Reorder the terms: -18 + -33x + 36x2 = 0 Solving -18 + -33x + 36x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-6 + -11x + 12x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-6 + -11x + 12x2)' equal to zero and attempt to solve: Simplifying -6 + -11x + 12x2 = 0 Solving -6 + -11x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -0.5 + -0.9166666667x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -0.9166666667x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -0.9166666667x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -0.9166666667x + x2 = 0 + 0.5 -0.9166666667x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -0.9166666667x + x2 = 0.5 The x term is -0.9166666667x. Take half its coefficient (-0.4583333334). Square it (0.2100694445) and add it to both sides. Add '0.2100694445' to each side of the equation. -0.9166666667x + 0.2100694445 + x2 = 0.5 + 0.2100694445 Reorder the terms: 0.2100694445 + -0.9166666667x + x2 = 0.5 + 0.2100694445 Combine like terms: 0.5 + 0.2100694445 = 0.7100694445 0.2100694445 + -0.9166666667x + x2 = 0.7100694445 Factor a perfect square on the left side: (x + -0.4583333334)(x + -0.4583333334) = 0.7100694445 Calculate the square root of the right side: 0.842656184 Break this problem into two subproblems by setting (x + -0.4583333334) equal to 0.842656184 and -0.842656184.Subproblem 1
x + -0.4583333334 = 0.842656184 Simplifying x + -0.4583333334 = 0.842656184 Reorder the terms: -0.4583333334 + x = 0.842656184 Solving -0.4583333334 + x = 0.842656184 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4583333334' to each side of the equation. -0.4583333334 + 0.4583333334 + x = 0.842656184 + 0.4583333334 Combine like terms: -0.4583333334 + 0.4583333334 = 0.0000000000 0.0000000000 + x = 0.842656184 + 0.4583333334 x = 0.842656184 + 0.4583333334 Combine like terms: 0.842656184 + 0.4583333334 = 1.3009895174 x = 1.3009895174 Simplifying x = 1.3009895174Subproblem 2
x + -0.4583333334 = -0.842656184 Simplifying x + -0.4583333334 = -0.842656184 Reorder the terms: -0.4583333334 + x = -0.842656184 Solving -0.4583333334 + x = -0.842656184 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4583333334' to each side of the equation. -0.4583333334 + 0.4583333334 + x = -0.842656184 + 0.4583333334 Combine like terms: -0.4583333334 + 0.4583333334 = 0.0000000000 0.0000000000 + x = -0.842656184 + 0.4583333334 x = -0.842656184 + 0.4583333334 Combine like terms: -0.842656184 + 0.4583333334 = -0.3843228506 x = -0.3843228506 Simplifying x = -0.3843228506Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.3009895174, -0.3843228506}Solution
x = {1.3009895174, -0.3843228506}
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