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Simplifying x + x + x(x + 2) = 675 Reorder the terms: x + x + x(2 + x) = 675 x + x + (2 * x + x * x) = 675 x + x + (2x + x2) = 675 Combine like terms: x + x = 2x 2x + 2x + x2 = 675 Combine like terms: 2x + 2x = 4x 4x + x2 = 675 Solving 4x + x2 = 675 Solving for variable 'x'. Reorder the terms: -675 + 4x + x2 = 675 + -675 Combine like terms: 675 + -675 = 0 -675 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '675' to each side of the equation. -675 + 4x + 675 + x2 = 0 + 675 Reorder the terms: -675 + 675 + 4x + x2 = 0 + 675 Combine like terms: -675 + 675 = 0 0 + 4x + x2 = 0 + 675 4x + x2 = 0 + 675 Combine like terms: 0 + 675 = 675 4x + x2 = 675 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 675 + 4 Reorder the terms: 4 + 4x + x2 = 675 + 4 Combine like terms: 675 + 4 = 679 4 + 4x + x2 = 679 Factor a perfect square on the left side: (x + 2)(x + 2) = 679 Calculate the square root of the right side: 26.057628442 Break this problem into two subproblems by setting (x + 2) equal to 26.057628442 and -26.057628442.Subproblem 1
x + 2 = 26.057628442 Simplifying x + 2 = 26.057628442 Reorder the terms: 2 + x = 26.057628442 Solving 2 + x = 26.057628442 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 26.057628442 + -2 Combine like terms: 2 + -2 = 0 0 + x = 26.057628442 + -2 x = 26.057628442 + -2 Combine like terms: 26.057628442 + -2 = 24.057628442 x = 24.057628442 Simplifying x = 24.057628442Subproblem 2
x + 2 = -26.057628442 Simplifying x + 2 = -26.057628442 Reorder the terms: 2 + x = -26.057628442 Solving 2 + x = -26.057628442 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -26.057628442 + -2 Combine like terms: 2 + -2 = 0 0 + x = -26.057628442 + -2 x = -26.057628442 + -2 Combine like terms: -26.057628442 + -2 = -28.057628442 x = -28.057628442 Simplifying x = -28.057628442Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.057628442, -28.057628442}
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