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Simplifying (2x + 1) * x = 600 Reorder the terms: (1 + 2x) * x = 600 Reorder the terms for easier multiplication: x(1 + 2x) = 600 (1 * x + 2x * x) = 600 (1x + 2x2) = 600 Solving 1x + 2x2 = 600 Solving for variable 'x'. Reorder the terms: -600 + 1x + 2x2 = 600 + -600 Combine like terms: 600 + -600 = 0 -600 + 1x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -300 + 0.5x + x2 = 0 Move the constant term to the right: Add '300' to each side of the equation. -300 + 0.5x + 300 + x2 = 0 + 300 Reorder the terms: -300 + 300 + 0.5x + x2 = 0 + 300 Combine like terms: -300 + 300 = 0 0 + 0.5x + x2 = 0 + 300 0.5x + x2 = 0 + 300 Combine like terms: 0 + 300 = 300 0.5x + x2 = 300 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 300 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 300 + 0.0625 Combine like terms: 300 + 0.0625 = 300.0625 0.0625 + 0.5x + x2 = 300.0625 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 300.0625 Calculate the square root of the right side: 17.322312201 Break this problem into two subproblems by setting (x + 0.25) equal to 17.322312201 and -17.322312201.Subproblem 1
x + 0.25 = 17.322312201 Simplifying x + 0.25 = 17.322312201 Reorder the terms: 0.25 + x = 17.322312201 Solving 0.25 + x = 17.322312201 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 17.322312201 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 17.322312201 + -0.25 x = 17.322312201 + -0.25 Combine like terms: 17.322312201 + -0.25 = 17.072312201 x = 17.072312201 Simplifying x = 17.072312201Subproblem 2
x + 0.25 = -17.322312201 Simplifying x + 0.25 = -17.322312201 Reorder the terms: 0.25 + x = -17.322312201 Solving 0.25 + x = -17.322312201 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -17.322312201 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -17.322312201 + -0.25 x = -17.322312201 + -0.25 Combine like terms: -17.322312201 + -0.25 = -17.572312201 x = -17.572312201 Simplifying x = -17.572312201Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.072312201, -17.572312201}
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