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Simplifying x2 + 27x + 56 = 0 Reorder the terms: 56 + 27x + x2 = 0 Solving 56 + 27x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-56' to each side of the equation. 56 + 27x + -56 + x2 = 0 + -56 Reorder the terms: 56 + -56 + 27x + x2 = 0 + -56 Combine like terms: 56 + -56 = 0 0 + 27x + x2 = 0 + -56 27x + x2 = 0 + -56 Combine like terms: 0 + -56 = -56 27x + x2 = -56 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 = -56 + 182.25 Reorder the terms: 182.25 + 27x + x2 = -56 + 182.25 Combine like terms: -56 + 182.25 = 126.25 182.25 + 27x + x2 = 126.25 Factor a perfect square on the left side: (x + 13.5)(x + 13.5) = 126.25 Calculate the square root of the right side: 11.236102527 Break this problem into two subproblems by setting (x + 13.5) equal to 11.236102527 and -11.236102527.Subproblem 1
x + 13.5 = 11.236102527 Simplifying x + 13.5 = 11.236102527 Reorder the terms: 13.5 + x = 11.236102527 Solving 13.5 + x = 11.236102527 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 = 11.236102527 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + x = 11.236102527 + -13.5 x = 11.236102527 + -13.5 Combine like terms: 11.236102527 + -13.5 = -2.263897473 x = -2.263897473 Simplifying x = -2.263897473Subproblem 2
x + 13.5 = -11.236102527 Simplifying x + 13.5 = -11.236102527 Reorder the terms: 13.5 + x = -11.236102527 Solving 13.5 + x = -11.236102527 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 = -11.236102527 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + x = -11.236102527 + -13.5 x = -11.236102527 + -13.5 Combine like terms: -11.236102527 + -13.5 = -24.736102527 x = -24.736102527 Simplifying x = -24.736102527Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.263897473, -24.736102527}
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