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Simplifying x(x + 3) = 200 Reorder the terms: x(3 + x) = 200 (3 * x + x * x) = 200 (3x + x2) = 200 Solving 3x + x2 = 200 Solving for variable 'x'. Reorder the terms: -200 + 3x + x2 = 200 + -200 Combine like terms: 200 + -200 = 0 -200 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '200' to each side of the equation. -200 + 3x + 200 + x2 = 0 + 200 Reorder the terms: -200 + 200 + 3x + x2 = 0 + 200 Combine like terms: -200 + 200 = 0 0 + 3x + x2 = 0 + 200 3x + x2 = 0 + 200 Combine like terms: 0 + 200 = 200 3x + x2 = 200 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 = 200 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 200 + 2.25 Combine like terms: 200 + 2.25 = 202.25 2.25 + 3x + x2 = 202.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 202.25 Calculate the square root of the right side: 14.221462653 Break this problem into two subproblems by setting (x + 1.5) equal to 14.221462653 and -14.221462653.Subproblem 1
x + 1.5 = 14.221462653 Simplifying x + 1.5 = 14.221462653 Reorder the terms: 1.5 + x = 14.221462653 Solving 1.5 + x = 14.221462653 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 = 14.221462653 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 14.221462653 + -1.5 x = 14.221462653 + -1.5 Combine like terms: 14.221462653 + -1.5 = 12.721462653 x = 12.721462653 Simplifying x = 12.721462653Subproblem 2
x + 1.5 = -14.221462653 Simplifying x + 1.5 = -14.221462653 Reorder the terms: 1.5 + x = -14.221462653 Solving 1.5 + x = -14.221462653 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 = -14.221462653 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -14.221462653 + -1.5 x = -14.221462653 + -1.5 Combine like terms: -14.221462653 + -1.5 = -15.721462653 x = -15.721462653 Simplifying x = -15.721462653Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.721462653, -15.721462653}
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