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Simplifying x2 + -14x + -13 = x Reorder the terms: -13 + -14x + x2 = x Solving -13 + -14x + x2 = x Solving for variable 'x'. Reorder the terms: -13 + -14x + -1x + x2 = x + -1x Combine like terms: -14x + -1x = -15x -13 + -15x + x2 = x + -1x Combine like terms: x + -1x = 0 -13 + -15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + -15x + 13 + x2 = 0 + 13 Reorder the terms: -13 + 13 + -15x + x2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -15x + x2 = 0 + 13 -15x + x2 = 0 + 13 Combine like terms: 0 + 13 = 13 -15x + x2 = 13 The x term is -15x. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15x + 56.25 + x2 = 13 + 56.25 Reorder the terms: 56.25 + -15x + x2 = 13 + 56.25 Combine like terms: 13 + 56.25 = 69.25 56.25 + -15x + x2 = 69.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 69.25 Calculate the square root of the right side: 8.321658489 Break this problem into two subproblems by setting (x + -7.5) equal to 8.321658489 and -8.321658489.Subproblem 1
x + -7.5 = 8.321658489 Simplifying x + -7.5 = 8.321658489 Reorder the terms: -7.5 + x = 8.321658489 Solving -7.5 + x = 8.321658489 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 8.321658489 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 8.321658489 + 7.5 x = 8.321658489 + 7.5 Combine like terms: 8.321658489 + 7.5 = 15.821658489 x = 15.821658489 Simplifying x = 15.821658489Subproblem 2
x + -7.5 = -8.321658489 Simplifying x + -7.5 = -8.321658489 Reorder the terms: -7.5 + x = -8.321658489 Solving -7.5 + x = -8.321658489 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -8.321658489 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -8.321658489 + 7.5 x = -8.321658489 + 7.5 Combine like terms: -8.321658489 + 7.5 = -0.821658489 x = -0.821658489 Simplifying x = -0.821658489Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.821658489, -0.821658489}
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