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Simplifying x(x + 2) = 15x + 102 Reorder the terms: x(2 + x) = 15x + 102 (2 * x + x * x) = 15x + 102 (2x + x2) = 15x + 102 Reorder the terms: 2x + x2 = 102 + 15x Solving 2x + x2 = 102 + 15x Solving for variable 'x'. Reorder the terms: -102 + 2x + -15x + x2 = 102 + 15x + -102 + -15x Combine like terms: 2x + -15x = -13x -102 + -13x + x2 = 102 + 15x + -102 + -15x Reorder the terms: -102 + -13x + x2 = 102 + -102 + 15x + -15x Combine like terms: 102 + -102 = 0 -102 + -13x + x2 = 0 + 15x + -15x -102 + -13x + x2 = 15x + -15x Combine like terms: 15x + -15x = 0 -102 + -13x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '102' to each side of the equation. -102 + -13x + 102 + x2 = 0 + 102 Reorder the terms: -102 + 102 + -13x + x2 = 0 + 102 Combine like terms: -102 + 102 = 0 0 + -13x + x2 = 0 + 102 -13x + x2 = 0 + 102 Combine like terms: 0 + 102 = 102 -13x + x2 = 102 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 = 102 + 42.25 Reorder the terms: 42.25 + -13x + x2 = 102 + 42.25 Combine like terms: 102 + 42.25 = 144.25 42.25 + -13x + x2 = 144.25 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 144.25 Calculate the square root of the right side: 12.010412149 Break this problem into two subproblems by setting (x + -6.5) equal to 12.010412149 and -12.010412149.Subproblem 1
x + -6.5 = 12.010412149 Simplifying x + -6.5 = 12.010412149 Reorder the terms: -6.5 + x = 12.010412149 Solving -6.5 + x = 12.010412149 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 = 12.010412149 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 12.010412149 + 6.5 x = 12.010412149 + 6.5 Combine like terms: 12.010412149 + 6.5 = 18.510412149 x = 18.510412149 Simplifying x = 18.510412149Subproblem 2
x + -6.5 = -12.010412149 Simplifying x + -6.5 = -12.010412149 Reorder the terms: -6.5 + x = -12.010412149 Solving -6.5 + x = -12.010412149 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 = -12.010412149 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -12.010412149 + 6.5 x = -12.010412149 + 6.5 Combine like terms: -12.010412149 + 6.5 = -5.510412149 x = -5.510412149 Simplifying x = -5.510412149Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.510412149, -5.510412149}
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