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Simplifying 2x2 + 2x + -108 = 0 Reorder the terms: -108 + 2x + 2x2 = 0 Solving -108 + 2x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-54 + x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-54 + x + x2)' equal to zero and attempt to solve: Simplifying -54 + x + x2 = 0 Solving -54 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '54' to each side of the equation. -54 + x + 54 + x2 = 0 + 54 Reorder the terms: -54 + 54 + x + x2 = 0 + 54 Combine like terms: -54 + 54 = 0 0 + x + x2 = 0 + 54 x + x2 = 0 + 54 Combine like terms: 0 + 54 = 54 x + x2 = 54 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = 54 + 0.25 Reorder the terms: 0.25 + x + x2 = 54 + 0.25 Combine like terms: 54 + 0.25 = 54.25 0.25 + x + x2 = 54.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 54.25 Calculate the square root of the right side: 7.365459931 Break this problem into two subproblems by setting (x + 0.5) equal to 7.365459931 and -7.365459931.Subproblem 1
x + 0.5 = 7.365459931 Simplifying x + 0.5 = 7.365459931 Reorder the terms: 0.5 + x = 7.365459931 Solving 0.5 + x = 7.365459931 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 7.365459931 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 7.365459931 + -0.5 x = 7.365459931 + -0.5 Combine like terms: 7.365459931 + -0.5 = 6.865459931 x = 6.865459931 Simplifying x = 6.865459931Subproblem 2
x + 0.5 = -7.365459931 Simplifying x + 0.5 = -7.365459931 Reorder the terms: 0.5 + x = -7.365459931 Solving 0.5 + x = -7.365459931 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -7.365459931 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -7.365459931 + -0.5 x = -7.365459931 + -0.5 Combine like terms: -7.365459931 + -0.5 = -7.865459931 x = -7.865459931 Simplifying x = -7.865459931Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.865459931, -7.865459931}Solution
x = {6.865459931, -7.865459931}
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