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Simplifying 13x + -5 = 4x + -1x2 + -14 Reorder the terms: -5 + 13x = 4x + -1x2 + -14 Reorder the terms: -5 + 13x = -14 + 4x + -1x2 Solving -5 + 13x = -14 + 4x + -1x2 Solving for variable 'x'. Reorder the terms: -5 + 14 + 13x + -4x + x2 = -14 + 4x + -1x2 + 14 + -4x + x2 Combine like terms: -5 + 14 = 9 9 + 13x + -4x + x2 = -14 + 4x + -1x2 + 14 + -4x + x2 Combine like terms: 13x + -4x = 9x 9 + 9x + x2 = -14 + 4x + -1x2 + 14 + -4x + x2 Reorder the terms: 9 + 9x + x2 = -14 + 14 + 4x + -4x + -1x2 + x2 Combine like terms: -14 + 14 = 0 9 + 9x + x2 = 0 + 4x + -4x + -1x2 + x2 9 + 9x + x2 = 4x + -4x + -1x2 + x2 Combine like terms: 4x + -4x = 0 9 + 9x + x2 = 0 + -1x2 + x2 9 + 9x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 9 + 9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + 9x + -9 + x2 = 0 + -9 Reorder the terms: 9 + -9 + 9x + x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 9x + x2 = 0 + -9 9x + x2 = 0 + -9 Combine like terms: 0 + -9 = -9 9x + x2 = -9 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = -9 + 20.25 Reorder the terms: 20.25 + 9x + x2 = -9 + 20.25 Combine like terms: -9 + 20.25 = 11.25 20.25 + 9x + x2 = 11.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 11.25 Calculate the square root of the right side: 3.354101966 Break this problem into two subproblems by setting (x + 4.5) equal to 3.354101966 and -3.354101966.Subproblem 1
x + 4.5 = 3.354101966 Simplifying x + 4.5 = 3.354101966 Reorder the terms: 4.5 + x = 3.354101966 Solving 4.5 + x = 3.354101966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 3.354101966 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 3.354101966 + -4.5 x = 3.354101966 + -4.5 Combine like terms: 3.354101966 + -4.5 = -1.145898034 x = -1.145898034 Simplifying x = -1.145898034Subproblem 2
x + 4.5 = -3.354101966 Simplifying x + 4.5 = -3.354101966 Reorder the terms: 4.5 + x = -3.354101966 Solving 4.5 + x = -3.354101966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -3.354101966 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -3.354101966 + -4.5 x = -3.354101966 + -4.5 Combine like terms: -3.354101966 + -4.5 = -7.854101966 x = -7.854101966 Simplifying x = -7.854101966Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.145898034, -7.854101966}
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