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Simplifying 0 = 51.68 + -1(14.4x) + -25.36x2 Remove parenthesis around (14.4x) 0 = 51.68 + -1 * 14.4x + -25.36x2 Multiply -1 * 14.4 0 = 51.68 + -14.4x + -25.36x2 Solving 0 = 51.68 + -14.4x + -25.36x2 Solving for variable 'x'. Combine like terms: 0 + -51.68 = -51.68 -51.68 + 14.4x + 25.36x2 = 51.68 + -14.4x + -25.36x2 + -51.68 + 14.4x + 25.36x2 Reorder the terms: -51.68 + 14.4x + 25.36x2 = 51.68 + -51.68 + -14.4x + 14.4x + -25.36x2 + 25.36x2 Combine like terms: 51.68 + -51.68 = 0.00 -51.68 + 14.4x + 25.36x2 = 0.00 + -14.4x + 14.4x + -25.36x2 + 25.36x2 -51.68 + 14.4x + 25.36x2 = -14.4x + 14.4x + -25.36x2 + 25.36x2 Combine like terms: -14.4x + 14.4x = 0.0 -51.68 + 14.4x + 25.36x2 = 0.0 + -25.36x2 + 25.36x2 -51.68 + 14.4x + 25.36x2 = -25.36x2 + 25.36x2 Combine like terms: -25.36x2 + 25.36x2 = 0.00 -51.68 + 14.4x + 25.36x2 = 0.00 Begin completing the square. Divide all terms by 25.36 the coefficient of the squared term: Divide each side by '25.36'. -2.03785489 + 0.5678233438x + x2 = 0 Move the constant term to the right: Add '2.03785489' to each side of the equation. -2.03785489 + 0.5678233438x + 2.03785489 + x2 = 0 + 2.03785489 Reorder the terms: -2.03785489 + 2.03785489 + 0.5678233438x + x2 = 0 + 2.03785489 Combine like terms: -2.03785489 + 2.03785489 = 0.00000000 0.00000000 + 0.5678233438x + x2 = 0 + 2.03785489 0.5678233438x + x2 = 0 + 2.03785489 Combine like terms: 0 + 2.03785489 = 2.03785489 0.5678233438x + x2 = 2.03785489 The x term is 0.5678233438x. Take half its coefficient (0.2839116719). Square it (0.08060583744) and add it to both sides. Add '0.08060583744' to each side of the equation. 0.5678233438x + 0.08060583744 + x2 = 2.03785489 + 0.08060583744 Reorder the terms: 0.08060583744 + 0.5678233438x + x2 = 2.03785489 + 0.08060583744 Combine like terms: 2.03785489 + 0.08060583744 = 2.11846072744 0.08060583744 + 0.5678233438x + x2 = 2.11846072744 Factor a perfect square on the left side: (x + 0.2839116719)(x + 0.2839116719) = 2.11846072744 Calculate the square root of the right side: 1.455493294 Break this problem into two subproblems by setting (x + 0.2839116719) equal to 1.455493294 and -1.455493294.Subproblem 1
x + 0.2839116719 = 1.455493294 Simplifying x + 0.2839116719 = 1.455493294 Reorder the terms: 0.2839116719 + x = 1.455493294 Solving 0.2839116719 + x = 1.455493294 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2839116719' to each side of the equation. 0.2839116719 + -0.2839116719 + x = 1.455493294 + -0.2839116719 Combine like terms: 0.2839116719 + -0.2839116719 = 0.0000000000 0.0000000000 + x = 1.455493294 + -0.2839116719 x = 1.455493294 + -0.2839116719 Combine like terms: 1.455493294 + -0.2839116719 = 1.1715816221 x = 1.1715816221 Simplifying x = 1.1715816221Subproblem 2
x + 0.2839116719 = -1.455493294 Simplifying x + 0.2839116719 = -1.455493294 Reorder the terms: 0.2839116719 + x = -1.455493294 Solving 0.2839116719 + x = -1.455493294 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2839116719' to each side of the equation. 0.2839116719 + -0.2839116719 + x = -1.455493294 + -0.2839116719 Combine like terms: 0.2839116719 + -0.2839116719 = 0.0000000000 0.0000000000 + x = -1.455493294 + -0.2839116719 x = -1.455493294 + -0.2839116719 Combine like terms: -1.455493294 + -0.2839116719 = -1.7394049659 x = -1.7394049659 Simplifying x = -1.7394049659Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1715816221, -1.7394049659}
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