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Simplifying (2x + 9) * x = 220 Reorder the terms: (9 + 2x) * x = 220 Reorder the terms for easier multiplication: x(9 + 2x) = 220 (9 * x + 2x * x) = 220 (9x + 2x2) = 220 Solving 9x + 2x2 = 220 Solving for variable 'x'. Reorder the terms: -220 + 9x + 2x2 = 220 + -220 Combine like terms: 220 + -220 = 0 -220 + 9x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -110 + 4.5x + x2 = 0 Move the constant term to the right: Add '110' to each side of the equation. -110 + 4.5x + 110 + x2 = 0 + 110 Reorder the terms: -110 + 110 + 4.5x + x2 = 0 + 110 Combine like terms: -110 + 110 = 0 0 + 4.5x + x2 = 0 + 110 4.5x + x2 = 0 + 110 Combine like terms: 0 + 110 = 110 4.5x + x2 = 110 The x term is 4.5x. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5x + 5.0625 + x2 = 110 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = 110 + 5.0625 Combine like terms: 110 + 5.0625 = 115.0625 5.0625 + 4.5x + x2 = 115.0625 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 115.0625 Calculate the square root of the right side: 10.726718976 Break this problem into two subproblems by setting (x + 2.25) equal to 10.726718976 and -10.726718976.Subproblem 1
x + 2.25 = 10.726718976 Simplifying x + 2.25 = 10.726718976 Reorder the terms: 2.25 + x = 10.726718976 Solving 2.25 + x = 10.726718976 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = 10.726718976 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 10.726718976 + -2.25 x = 10.726718976 + -2.25 Combine like terms: 10.726718976 + -2.25 = 8.476718976 x = 8.476718976 Simplifying x = 8.476718976Subproblem 2
x + 2.25 = -10.726718976 Simplifying x + 2.25 = -10.726718976 Reorder the terms: 2.25 + x = -10.726718976 Solving 2.25 + x = -10.726718976 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = -10.726718976 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -10.726718976 + -2.25 x = -10.726718976 + -2.25 Combine like terms: -10.726718976 + -2.25 = -12.976718976 x = -12.976718976 Simplifying x = -12.976718976Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.476718976, -12.976718976}
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