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Simplifying 3x2 + -33x = 72 Reorder the terms: -33x + 3x2 = 72 Solving -33x + 3x2 = 72 Solving for variable 'x'. Reorder the terms: -72 + -33x + 3x2 = 72 + -72 Combine like terms: 72 + -72 = 0 -72 + -33x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-24 + -11x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-24 + -11x + x2)' equal to zero and attempt to solve: Simplifying -24 + -11x + x2 = 0 Solving -24 + -11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '24' to each side of the equation. -24 + -11x + 24 + x2 = 0 + 24 Reorder the terms: -24 + 24 + -11x + x2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -11x + x2 = 0 + 24 -11x + x2 = 0 + 24 Combine like terms: 0 + 24 = 24 -11x + x2 = 24 The x term is -11x. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11x + 30.25 + x2 = 24 + 30.25 Reorder the terms: 30.25 + -11x + x2 = 24 + 30.25 Combine like terms: 24 + 30.25 = 54.25 30.25 + -11x + x2 = 54.25 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 54.25 Calculate the square root of the right side: 7.365459931 Break this problem into two subproblems by setting (x + -5.5) equal to 7.365459931 and -7.365459931.Subproblem 1
x + -5.5 = 7.365459931 Simplifying x + -5.5 = 7.365459931 Reorder the terms: -5.5 + x = 7.365459931 Solving -5.5 + x = 7.365459931 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = 7.365459931 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 7.365459931 + 5.5 x = 7.365459931 + 5.5 Combine like terms: 7.365459931 + 5.5 = 12.865459931 x = 12.865459931 Simplifying x = 12.865459931Subproblem 2
x + -5.5 = -7.365459931 Simplifying x + -5.5 = -7.365459931 Reorder the terms: -5.5 + x = -7.365459931 Solving -5.5 + x = -7.365459931 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = -7.365459931 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -7.365459931 + 5.5 x = -7.365459931 + 5.5 Combine like terms: -7.365459931 + 5.5 = -1.865459931 x = -1.865459931 Simplifying x = -1.865459931Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.865459931, -1.865459931}Solution
x = {12.865459931, -1.865459931}
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