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Simplifying x(2x + 45) = 1246 Reorder the terms: x(45 + 2x) = 1246 (45 * x + 2x * x) = 1246 (45x + 2x2) = 1246 Solving 45x + 2x2 = 1246 Solving for variable 'x'. Reorder the terms: -1246 + 45x + 2x2 = 1246 + -1246 Combine like terms: 1246 + -1246 = 0 -1246 + 45x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -623 + 22.5x + x2 = 0 Move the constant term to the right: Add '623' to each side of the equation. -623 + 22.5x + 623 + x2 = 0 + 623 Reorder the terms: -623 + 623 + 22.5x + x2 = 0 + 623 Combine like terms: -623 + 623 = 0 0 + 22.5x + x2 = 0 + 623 22.5x + x2 = 0 + 623 Combine like terms: 0 + 623 = 623 22.5x + x2 = 623 The x term is 22.5x. Take half its coefficient (11.25). Square it (126.5625) and add it to both sides. Add '126.5625' to each side of the equation. 22.5x + 126.5625 + x2 = 623 + 126.5625 Reorder the terms: 126.5625 + 22.5x + x2 = 623 + 126.5625 Combine like terms: 623 + 126.5625 = 749.5625 126.5625 + 22.5x + x2 = 749.5625 Factor a perfect square on the left side: (x + 11.25)(x + 11.25) = 749.5625 Calculate the square root of the right side: 27.378139089 Break this problem into two subproblems by setting (x + 11.25) equal to 27.378139089 and -27.378139089.Subproblem 1
x + 11.25 = 27.378139089 Simplifying x + 11.25 = 27.378139089 Reorder the terms: 11.25 + x = 27.378139089 Solving 11.25 + x = 27.378139089 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.25' to each side of the equation. 11.25 + -11.25 + x = 27.378139089 + -11.25 Combine like terms: 11.25 + -11.25 = 0.00 0.00 + x = 27.378139089 + -11.25 x = 27.378139089 + -11.25 Combine like terms: 27.378139089 + -11.25 = 16.128139089 x = 16.128139089 Simplifying x = 16.128139089Subproblem 2
x + 11.25 = -27.378139089 Simplifying x + 11.25 = -27.378139089 Reorder the terms: 11.25 + x = -27.378139089 Solving 11.25 + x = -27.378139089 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.25' to each side of the equation. 11.25 + -11.25 + x = -27.378139089 + -11.25 Combine like terms: 11.25 + -11.25 = 0.00 0.00 + x = -27.378139089 + -11.25 x = -27.378139089 + -11.25 Combine like terms: -27.378139089 + -11.25 = -38.628139089 x = -38.628139089 Simplifying x = -38.628139089Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.128139089, -38.628139089}
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