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Simplifying x2 + 2x2 = 81x + 162 Combine like terms: x2 + 2x2 = 3x2 3x2 = 81x + 162 Reorder the terms: 3x2 = 162 + 81x Solving 3x2 = 162 + 81x Solving for variable 'x'. Reorder the terms: -162 + -81x + 3x2 = 162 + 81x + -162 + -81x Reorder the terms: -162 + -81x + 3x2 = 162 + -162 + 81x + -81x Combine like terms: 162 + -162 = 0 -162 + -81x + 3x2 = 0 + 81x + -81x -162 + -81x + 3x2 = 81x + -81x Combine like terms: 81x + -81x = 0 -162 + -81x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-54 + -27x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-54 + -27x + x2)' equal to zero and attempt to solve: Simplifying -54 + -27x + x2 = 0 Solving -54 + -27x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '54' to each side of the equation. -54 + -27x + 54 + x2 = 0 + 54 Reorder the terms: -54 + 54 + -27x + x2 = 0 + 54 Combine like terms: -54 + 54 = 0 0 + -27x + x2 = 0 + 54 -27x + x2 = 0 + 54 Combine like terms: 0 + 54 = 54 -27x + x2 = 54 The x term is -27x. Take half its coefficient (-13.5). Square it (182.25) and add it to both sides. Add '182.25' to each side of the equation. -27x + 182.25 + x2 = 54 + 182.25 Reorder the terms: 182.25 + -27x + x2 = 54 + 182.25 Combine like terms: 54 + 182.25 = 236.25 182.25 + -27x + x2 = 236.25 Factor a perfect square on the left side: (x + -13.5)(x + -13.5) = 236.25 Calculate the square root of the right side: 15.370426149 Break this problem into two subproblems by setting (x + -13.5) equal to 15.370426149 and -15.370426149.Subproblem 1
x + -13.5 = 15.370426149 Simplifying x + -13.5 = 15.370426149 Reorder the terms: -13.5 + x = 15.370426149 Solving -13.5 + x = 15.370426149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.5' to each side of the equation. -13.5 + 13.5 + x = 15.370426149 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + x = 15.370426149 + 13.5 x = 15.370426149 + 13.5 Combine like terms: 15.370426149 + 13.5 = 28.870426149 x = 28.870426149 Simplifying x = 28.870426149Subproblem 2
x + -13.5 = -15.370426149 Simplifying x + -13.5 = -15.370426149 Reorder the terms: -13.5 + x = -15.370426149 Solving -13.5 + x = -15.370426149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.5' to each side of the equation. -13.5 + 13.5 + x = -15.370426149 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + x = -15.370426149 + 13.5 x = -15.370426149 + 13.5 Combine like terms: -15.370426149 + 13.5 = -1.870426149 x = -1.870426149 Simplifying x = -1.870426149Solution
The solution to the problem is based on the solutions from the subproblems. x = {28.870426149, -1.870426149}Solution
x = {28.870426149, -1.870426149}
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