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Simplifying x2 + 11x + -54 = 0 Reorder the terms: -54 + 11x + x2 = 0 Solving -54 + 11x + 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 + 11x + 54 + x2 = 0 + 54 Reorder the terms: -54 + 54 + 11x + x2 = 0 + 54 Combine like terms: -54 + 54 = 0 0 + 11x + x2 = 0 + 54 11x + x2 = 0 + 54 Combine like terms: 0 + 54 = 54 11x + x2 = 54 The x term is 11x. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11x + 30.25 + x2 = 54 + 30.25 Reorder the terms: 30.25 + 11x + x2 = 54 + 30.25 Combine like terms: 54 + 30.25 = 84.25 30.25 + 11x + x2 = 84.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 84.25 Calculate the square root of the right side: 9.178779875 Break this problem into two subproblems by setting (x + 5.5) equal to 9.178779875 and -9.178779875.Subproblem 1
x + 5.5 = 9.178779875 Simplifying x + 5.5 = 9.178779875 Reorder the terms: 5.5 + x = 9.178779875 Solving 5.5 + x = 9.178779875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = 9.178779875 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 9.178779875 + -5.5 x = 9.178779875 + -5.5 Combine like terms: 9.178779875 + -5.5 = 3.678779875 x = 3.678779875 Simplifying x = 3.678779875Subproblem 2
x + 5.5 = -9.178779875 Simplifying x + 5.5 = -9.178779875 Reorder the terms: 5.5 + x = -9.178779875 Solving 5.5 + x = -9.178779875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = -9.178779875 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -9.178779875 + -5.5 x = -9.178779875 + -5.5 Combine like terms: -9.178779875 + -5.5 = -14.678779875 x = -14.678779875 Simplifying x = -14.678779875Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.678779875, -14.678779875}
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