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Simplifying x2 + 27x + -4 = 0 Reorder the terms: -4 + 27x + x2 = 0 Solving -4 + 27x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + 27x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 27x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 27x + x2 = 0 + 4 27x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 27x + x2 = 4 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 = 4 + 182.25 Reorder the terms: 182.25 + 27x + x2 = 4 + 182.25 Combine like terms: 4 + 182.25 = 186.25 182.25 + 27x + x2 = 186.25 Factor a perfect square on the left side: (x + 13.5)(x + 13.5) = 186.25 Calculate the square root of the right side: 13.647344064 Break this problem into two subproblems by setting (x + 13.5) equal to 13.647344064 and -13.647344064.Subproblem 1
x + 13.5 = 13.647344064 Simplifying x + 13.5 = 13.647344064 Reorder the terms: 13.5 + x = 13.647344064 Solving 13.5 + x = 13.647344064 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 = 13.647344064 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + x = 13.647344064 + -13.5 x = 13.647344064 + -13.5 Combine like terms: 13.647344064 + -13.5 = 0.147344064 x = 0.147344064 Simplifying x = 0.147344064Subproblem 2
x + 13.5 = -13.647344064 Simplifying x + 13.5 = -13.647344064 Reorder the terms: 13.5 + x = -13.647344064 Solving 13.5 + x = -13.647344064 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 = -13.647344064 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + x = -13.647344064 + -13.5 x = -13.647344064 + -13.5 Combine like terms: -13.647344064 + -13.5 = -27.147344064 x = -27.147344064 Simplifying x = -27.147344064Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.147344064, -27.147344064}
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