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Simplifying x2 + 13x = 96 Reorder the terms: 13x + x2 = 96 Solving 13x + x2 = 96 Solving for variable 'x'. Reorder the terms: -96 + 13x + x2 = 96 + -96 Combine like terms: 96 + -96 = 0 -96 + 13x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '96' to each side of the equation. -96 + 13x + 96 + x2 = 0 + 96 Reorder the terms: -96 + 96 + 13x + x2 = 0 + 96 Combine like terms: -96 + 96 = 0 0 + 13x + x2 = 0 + 96 13x + x2 = 0 + 96 Combine like terms: 0 + 96 = 96 13x + x2 = 96 The x term is 13x. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13x + 42.25 + x2 = 96 + 42.25 Reorder the terms: 42.25 + 13x + x2 = 96 + 42.25 Combine like terms: 96 + 42.25 = 138.25 42.25 + 13x + x2 = 138.25 Factor a perfect square on the left side: (x + 6.5)(x + 6.5) = 138.25 Calculate the square root of the right side: 11.757976016 Break this problem into two subproblems by setting (x + 6.5) equal to 11.757976016 and -11.757976016.Subproblem 1
x + 6.5 = 11.757976016 Simplifying x + 6.5 = 11.757976016 Reorder the terms: 6.5 + x = 11.757976016 Solving 6.5 + x = 11.757976016 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = 11.757976016 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 11.757976016 + -6.5 x = 11.757976016 + -6.5 Combine like terms: 11.757976016 + -6.5 = 5.257976016 x = 5.257976016 Simplifying x = 5.257976016Subproblem 2
x + 6.5 = -11.757976016 Simplifying x + 6.5 = -11.757976016 Reorder the terms: 6.5 + x = -11.757976016 Solving 6.5 + x = -11.757976016 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = -11.757976016 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -11.757976016 + -6.5 x = -11.757976016 + -6.5 Combine like terms: -11.757976016 + -6.5 = -18.257976016 x = -18.257976016 Simplifying x = -18.257976016Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.257976016, -18.257976016}
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