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Simplifying 13x = 19 + -1x2 Solving 13x = 19 + -1x2 Solving for variable 'x'. Reorder the terms: -19 + 13x + x2 = 19 + -1x2 + -19 + x2 Reorder the terms: -19 + 13x + x2 = 19 + -19 + -1x2 + x2 Combine like terms: 19 + -19 = 0 -19 + 13x + x2 = 0 + -1x2 + x2 -19 + 13x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -19 + 13x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '19' to each side of the equation. -19 + 13x + 19 + x2 = 0 + 19 Reorder the terms: -19 + 19 + 13x + x2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + 13x + x2 = 0 + 19 13x + x2 = 0 + 19 Combine like terms: 0 + 19 = 19 13x + x2 = 19 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 = 19 + 42.25 Reorder the terms: 42.25 + 13x + x2 = 19 + 42.25 Combine like terms: 19 + 42.25 = 61.25 42.25 + 13x + x2 = 61.25 Factor a perfect square on the left side: (x + 6.5)(x + 6.5) = 61.25 Calculate the square root of the right side: 7.826237921 Break this problem into two subproblems by setting (x + 6.5) equal to 7.826237921 and -7.826237921.Subproblem 1
x + 6.5 = 7.826237921 Simplifying x + 6.5 = 7.826237921 Reorder the terms: 6.5 + x = 7.826237921 Solving 6.5 + x = 7.826237921 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 = 7.826237921 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 7.826237921 + -6.5 x = 7.826237921 + -6.5 Combine like terms: 7.826237921 + -6.5 = 1.326237921 x = 1.326237921 Simplifying x = 1.326237921Subproblem 2
x + 6.5 = -7.826237921 Simplifying x + 6.5 = -7.826237921 Reorder the terms: 6.5 + x = -7.826237921 Solving 6.5 + x = -7.826237921 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 = -7.826237921 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -7.826237921 + -6.5 x = -7.826237921 + -6.5 Combine like terms: -7.826237921 + -6.5 = -14.326237921 x = -14.326237921 Simplifying x = -14.326237921Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.326237921, -14.326237921}
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