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Simplifying x + -15 + x(x + -15) = x Reorder the terms: x + -15 + x(-15 + x) = x x + -15 + (-15 * x + x * x) = x x + -15 + (-15x + x2) = x Reorder the terms: -15 + x + -15x + x2 = x Combine like terms: x + -15x = -14x -15 + -14x + x2 = x Solving -15 + -14x + x2 = x Solving for variable 'x'. Reorder the terms: -15 + -14x + -1x + x2 = x + -1x Combine like terms: -14x + -1x = -15x -15 + -15x + x2 = x + -1x Combine like terms: x + -1x = 0 -15 + -15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + -15x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + -15x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -15x + x2 = 0 + 15 -15x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 -15x + x2 = 15 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 = 15 + 56.25 Reorder the terms: 56.25 + -15x + x2 = 15 + 56.25 Combine like terms: 15 + 56.25 = 71.25 56.25 + -15x + x2 = 71.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 71.25 Calculate the square root of the right side: 8.440971508 Break this problem into two subproblems by setting (x + -7.5) equal to 8.440971508 and -8.440971508.Subproblem 1
x + -7.5 = 8.440971508 Simplifying x + -7.5 = 8.440971508 Reorder the terms: -7.5 + x = 8.440971508 Solving -7.5 + x = 8.440971508 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 = 8.440971508 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 8.440971508 + 7.5 x = 8.440971508 + 7.5 Combine like terms: 8.440971508 + 7.5 = 15.940971508 x = 15.940971508 Simplifying x = 15.940971508Subproblem 2
x + -7.5 = -8.440971508 Simplifying x + -7.5 = -8.440971508 Reorder the terms: -7.5 + x = -8.440971508 Solving -7.5 + x = -8.440971508 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 = -8.440971508 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -8.440971508 + 7.5 x = -8.440971508 + 7.5 Combine like terms: -8.440971508 + 7.5 = -0.940971508 x = -0.940971508 Simplifying x = -0.940971508Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.940971508, -0.940971508}
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