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Simplifying 24X2 + -22X + -66 = 0 Reorder the terms: -66 + -22X + 24X2 = 0 Solving -66 + -22X + 24X2 = 0 Solving for variable 'X'. Factor out the Greatest Common Factor (GCF), '2'. 2(-33 + -11X + 12X2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-33 + -11X + 12X2)' equal to zero and attempt to solve: Simplifying -33 + -11X + 12X2 = 0 Solving -33 + -11X + 12X2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -2.75 + -0.9166666667X + X2 = 0 Move the constant term to the right: Add '2.75' to each side of the equation. -2.75 + -0.9166666667X + 2.75 + X2 = 0 + 2.75 Reorder the terms: -2.75 + 2.75 + -0.9166666667X + X2 = 0 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + -0.9166666667X + X2 = 0 + 2.75 -0.9166666667X + X2 = 0 + 2.75 Combine like terms: 0 + 2.75 = 2.75 -0.9166666667X + X2 = 2.75 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 = 2.75 + 0.2100694445 Reorder the terms: 0.2100694445 + -0.9166666667X + X2 = 2.75 + 0.2100694445 Combine like terms: 2.75 + 0.2100694445 = 2.9600694445 0.2100694445 + -0.9166666667X + X2 = 2.9600694445 Factor a perfect square on the left side: (X + -0.4583333334)(X + -0.4583333334) = 2.9600694445 Calculate the square root of the right side: 1.720485235 Break this problem into two subproblems by setting (X + -0.4583333334) equal to 1.720485235 and -1.720485235.Subproblem 1
X + -0.4583333334 = 1.720485235 Simplifying X + -0.4583333334 = 1.720485235 Reorder the terms: -0.4583333334 + X = 1.720485235 Solving -0.4583333334 + X = 1.720485235 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 = 1.720485235 + 0.4583333334 Combine like terms: -0.4583333334 + 0.4583333334 = 0.0000000000 0.0000000000 + X = 1.720485235 + 0.4583333334 X = 1.720485235 + 0.4583333334 Combine like terms: 1.720485235 + 0.4583333334 = 2.1788185684 X = 2.1788185684 Simplifying X = 2.1788185684Subproblem 2
X + -0.4583333334 = -1.720485235 Simplifying X + -0.4583333334 = -1.720485235 Reorder the terms: -0.4583333334 + X = -1.720485235 Solving -0.4583333334 + X = -1.720485235 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 = -1.720485235 + 0.4583333334 Combine like terms: -0.4583333334 + 0.4583333334 = 0.0000000000 0.0000000000 + X = -1.720485235 + 0.4583333334 X = -1.720485235 + 0.4583333334 Combine like terms: -1.720485235 + 0.4583333334 = -1.2621519016 X = -1.2621519016 Simplifying X = -1.2621519016Solution
The solution to the problem is based on the solutions from the subproblems. X = {2.1788185684, -1.2621519016}Solution
X = {2.1788185684, -1.2621519016}
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