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Simplifying x + x(x + 2) = 675 Reorder the terms: x + x(2 + x) = 675 x + (2 * x + x * x) = 675 x + (2x + x2) = 675 Combine like terms: x + 2x = 3x 3x + x2 = 675 Solving 3x + x2 = 675 Solving for variable 'x'. Reorder the terms: -675 + 3x + x2 = 675 + -675 Combine like terms: 675 + -675 = 0 -675 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '675' to each side of the equation. -675 + 3x + 675 + x2 = 0 + 675 Reorder the terms: -675 + 675 + 3x + x2 = 0 + 675 Combine like terms: -675 + 675 = 0 0 + 3x + x2 = 0 + 675 3x + x2 = 0 + 675 Combine like terms: 0 + 675 = 675 3x + x2 = 675 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 675 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 675 + 2.25 Combine like terms: 675 + 2.25 = 677.25 2.25 + 3x + x2 = 677.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 677.25 Calculate the square root of the right side: 26.024027359 Break this problem into two subproblems by setting (x + 1.5) equal to 26.024027359 and -26.024027359.Subproblem 1
x + 1.5 = 26.024027359 Simplifying x + 1.5 = 26.024027359 Reorder the terms: 1.5 + x = 26.024027359 Solving 1.5 + x = 26.024027359 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 26.024027359 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 26.024027359 + -1.5 x = 26.024027359 + -1.5 Combine like terms: 26.024027359 + -1.5 = 24.524027359 x = 24.524027359 Simplifying x = 24.524027359Subproblem 2
x + 1.5 = -26.024027359 Simplifying x + 1.5 = -26.024027359 Reorder the terms: 1.5 + x = -26.024027359 Solving 1.5 + x = -26.024027359 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -26.024027359 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -26.024027359 + -1.5 x = -26.024027359 + -1.5 Combine like terms: -26.024027359 + -1.5 = -27.524027359 x = -27.524027359 Simplifying x = -27.524027359Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.524027359, -27.524027359}
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