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Simplifying x2 + 29x + -960 = 0 Reorder the terms: -960 + 29x + x2 = 0 Solving -960 + 29x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '960' to each side of the equation. -960 + 29x + 960 + x2 = 0 + 960 Reorder the terms: -960 + 960 + 29x + x2 = 0 + 960 Combine like terms: -960 + 960 = 0 0 + 29x + x2 = 0 + 960 29x + x2 = 0 + 960 Combine like terms: 0 + 960 = 960 29x + x2 = 960 The x term is 29x. Take half its coefficient (14.5). Square it (210.25) and add it to both sides. Add '210.25' to each side of the equation. 29x + 210.25 + x2 = 960 + 210.25 Reorder the terms: 210.25 + 29x + x2 = 960 + 210.25 Combine like terms: 960 + 210.25 = 1170.25 210.25 + 29x + x2 = 1170.25 Factor a perfect square on the left side: (x + 14.5)(x + 14.5) = 1170.25 Calculate the square root of the right side: 34.208916966 Break this problem into two subproblems by setting (x + 14.5) equal to 34.208916966 and -34.208916966.Subproblem 1
x + 14.5 = 34.208916966 Simplifying x + 14.5 = 34.208916966 Reorder the terms: 14.5 + x = 34.208916966 Solving 14.5 + x = 34.208916966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14.5' to each side of the equation. 14.5 + -14.5 + x = 34.208916966 + -14.5 Combine like terms: 14.5 + -14.5 = 0.0 0.0 + x = 34.208916966 + -14.5 x = 34.208916966 + -14.5 Combine like terms: 34.208916966 + -14.5 = 19.708916966 x = 19.708916966 Simplifying x = 19.708916966Subproblem 2
x + 14.5 = -34.208916966 Simplifying x + 14.5 = -34.208916966 Reorder the terms: 14.5 + x = -34.208916966 Solving 14.5 + x = -34.208916966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14.5' to each side of the equation. 14.5 + -14.5 + x = -34.208916966 + -14.5 Combine like terms: 14.5 + -14.5 = 0.0 0.0 + x = -34.208916966 + -14.5 x = -34.208916966 + -14.5 Combine like terms: -34.208916966 + -14.5 = -48.708916966 x = -48.708916966 Simplifying x = -48.708916966Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.708916966, -48.708916966}
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