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Simplifying 2x2 + 22x + -48 = 0 Reorder the terms: -48 + 22x + 2x2 = 0 Solving -48 + 22x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-24 + 11x + x2) = 0 Ignore the factor 2.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 = 1.865459931 x = 1.865459931 Simplifying x = 1.865459931Subproblem 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 = -12.865459931 x = -12.865459931 Simplifying x = -12.865459931Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.865459931, -12.865459931}Solution
x = {1.865459931, -12.865459931}
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