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Simplifying (2x2) + x + -27 = 0 Reorder the terms: -27 + x + (2x2) = 0 Solving -27 + x + (2x2) = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -13.5 + 0.5x + x2 = 0 Move the constant term to the right: Add '13.5' to each side of the equation. -13.5 + 0.5x + 13.5 + x2 = 0 + 13.5 Reorder the terms: -13.5 + 13.5 + 0.5x + x2 = 0 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + 0.5x + x2 = 0 + 13.5 0.5x + x2 = 0 + 13.5 Combine like terms: 0 + 13.5 = 13.5 0.5x + x2 = 13.5 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.5x + 0.25 + x2 = 13.5 + 0.25 Reorder the terms: 0.25 + 0.5x + x2 = 13.5 + 0.25 Combine like terms: 13.5 + 0.25 = 13.75 0.25 + 0.5x + x2 = 13.75 Factor a perfect square on the left side: ((x) + 0.5)((x) + 0.5) = 13.75 Calculate the square root of the right side: 3.708099244 Break this problem into two subproblems by setting ((x) + 0.5) equal to 3.708099244 and -3.708099244.Subproblem 1
(x) + 0.5 = 3.708099244 Simplifying (x) + 0.5 = 3.708099244 x + 0.5 = 3.708099244 Reorder the terms: 0.5 + x = 3.708099244 Solving 0.5 + x = 3.708099244 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 3.708099244 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 3.708099244 + -0.5 x = 3.708099244 + -0.5 Combine like terms: 3.708099244 + -0.5 = 3.208099244 x = 3.208099244 Simplifying x = 3.208099244Subproblem 2
(x) + 0.5 = -3.708099244 Simplifying (x) + 0.5 = -3.708099244 x + 0.5 = -3.708099244 Reorder the terms: 0.5 + x = -3.708099244 Solving 0.5 + x = -3.708099244 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -3.708099244 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -3.708099244 + -0.5 x = -3.708099244 + -0.5 Combine like terms: -3.708099244 + -0.5 = -4.208099244 x = -4.208099244 Simplifying x = -4.208099244Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.208099244, -4.208099244}
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