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Simplifying x2 + 27x + -54 = 0 Reorder the terms: -54 + 27x + x2 = 0 Solving -54 + 27x + x2 = 0 Solving for variable 'x'. 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 = 1.870426149 x = 1.870426149 Simplifying x = 1.870426149Subproblem 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 = -28.870426149 x = -28.870426149 Simplifying x = -28.870426149Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.870426149, -28.870426149}
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