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Simplifying x2 + 27x + 174.96 = 0 Reorder the terms: 174.96 + 27x + x2 = 0 Solving 174.96 + 27x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-174.96' to each side of the equation. 174.96 + 27x + -174.96 + x2 = 0 + -174.96 Reorder the terms: 174.96 + -174.96 + 27x + x2 = 0 + -174.96 Combine like terms: 174.96 + -174.96 = 0.00 0.00 + 27x + x2 = 0 + -174.96 27x + x2 = 0 + -174.96 Combine like terms: 0 + -174.96 = -174.96 27x + x2 = -174.96 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 = -174.96 + 182.25 Reorder the terms: 182.25 + 27x + x2 = -174.96 + 182.25 Combine like terms: -174.96 + 182.25 = 7.29 182.25 + 27x + x2 = 7.29 Factor a perfect square on the left side: (x + 13.5)(x + 13.5) = 7.29 Calculate the square root of the right side: 2.7 Break this problem into two subproblems by setting (x + 13.5) equal to 2.7 and -2.7.Subproblem 1
x + 13.5 = 2.7 Simplifying x + 13.5 = 2.7 Reorder the terms: 13.5 + x = 2.7 Solving 13.5 + x = 2.7 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 = 2.7 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + x = 2.7 + -13.5 x = 2.7 + -13.5 Combine like terms: 2.7 + -13.5 = -10.8 x = -10.8 Simplifying x = -10.8Subproblem 2
x + 13.5 = -2.7 Simplifying x + 13.5 = -2.7 Reorder the terms: 13.5 + x = -2.7 Solving 13.5 + x = -2.7 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 = -2.7 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + x = -2.7 + -13.5 x = -2.7 + -13.5 Combine like terms: -2.7 + -13.5 = -16.2 x = -16.2 Simplifying x = -16.2Solution
The solution to the problem is based on the solutions from the subproblems. x = {-10.8, -16.2}
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