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Simplifying (14 + 20) * 14 = (x + 25) * x Combine like terms: 14 + 20 = 34 (34) * 14 = (x + 25) * x Multiply 34 * 14 476 = (x + 25) * x Reorder the terms: 476 = (25 + x) * x Reorder the terms for easier multiplication: 476 = x(25 + x) 476 = (25 * x + x * x) 476 = (25x + x2) Solving 476 = 25x + x2 Solving for variable 'x'. Reorder the terms: 476 + -25x + -1x2 = 25x + -25x + x2 + -1x2 Combine like terms: 25x + -25x = 0 476 + -25x + -1x2 = 0 + x2 + -1x2 476 + -25x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 476 + -25x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -476 + 25x + x2 = 0 Move the constant term to the right: Add '476' to each side of the equation. -476 + 25x + 476 + x2 = 0 + 476 Reorder the terms: -476 + 476 + 25x + x2 = 0 + 476 Combine like terms: -476 + 476 = 0 0 + 25x + x2 = 0 + 476 25x + x2 = 0 + 476 Combine like terms: 0 + 476 = 476 25x + x2 = 476 The x term is 25x. Take half its coefficient (12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. 25x + 156.25 + x2 = 476 + 156.25 Reorder the terms: 156.25 + 25x + x2 = 476 + 156.25 Combine like terms: 476 + 156.25 = 632.25 156.25 + 25x + x2 = 632.25 Factor a perfect square on the left side: (x + 12.5)(x + 12.5) = 632.25 Calculate the square root of the right side: 25.144581921 Break this problem into two subproblems by setting (x + 12.5) equal to 25.144581921 and -25.144581921.Subproblem 1
x + 12.5 = 25.144581921 Simplifying x + 12.5 = 25.144581921 Reorder the terms: 12.5 + x = 25.144581921 Solving 12.5 + x = 25.144581921 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + x = 25.144581921 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = 25.144581921 + -12.5 x = 25.144581921 + -12.5 Combine like terms: 25.144581921 + -12.5 = 12.644581921 x = 12.644581921 Simplifying x = 12.644581921Subproblem 2
x + 12.5 = -25.144581921 Simplifying x + 12.5 = -25.144581921 Reorder the terms: 12.5 + x = -25.144581921 Solving 12.5 + x = -25.144581921 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + x = -25.144581921 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = -25.144581921 + -12.5 x = -25.144581921 + -12.5 Combine like terms: -25.144581921 + -12.5 = -37.644581921 x = -37.644581921 Simplifying x = -37.644581921Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.644581921, -37.644581921}
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