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Simplifying x2 + 27x + 29 = 0 Reorder the terms: 29 + 27x + x2 = 0 Solving 29 + 27x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-29' to each side of the equation. 29 + 27x + -29 + x2 = 0 + -29 Reorder the terms: 29 + -29 + 27x + x2 = 0 + -29 Combine like terms: 29 + -29 = 0 0 + 27x + x2 = 0 + -29 27x + x2 = 0 + -29 Combine like terms: 0 + -29 = -29 27x + x2 = -29 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 = -29 + 182.25 Reorder the terms: 182.25 + 27x + x2 = -29 + 182.25 Combine like terms: -29 + 182.25 = 153.25 182.25 + 27x + x2 = 153.25 Factor a perfect square on the left side: (x + 13.5)(x + 13.5) = 153.25 Calculate the square root of the right side: 12.379418403 Break this problem into two subproblems by setting (x + 13.5) equal to 12.379418403 and -12.379418403.Subproblem 1
x + 13.5 = 12.379418403 Simplifying x + 13.5 = 12.379418403 Reorder the terms: 13.5 + x = 12.379418403 Solving 13.5 + x = 12.379418403 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 = 12.379418403 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + x = 12.379418403 + -13.5 x = 12.379418403 + -13.5 Combine like terms: 12.379418403 + -13.5 = -1.120581597 x = -1.120581597 Simplifying x = -1.120581597Subproblem 2
x + 13.5 = -12.379418403 Simplifying x + 13.5 = -12.379418403 Reorder the terms: 13.5 + x = -12.379418403 Solving 13.5 + x = -12.379418403 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 = -12.379418403 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + x = -12.379418403 + -13.5 x = -12.379418403 + -13.5 Combine like terms: -12.379418403 + -13.5 = -25.879418403 x = -25.879418403 Simplifying x = -25.879418403Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.120581597, -25.879418403}
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