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Simplifying (x + 25)(x) = 326 Reorder the terms: (25 + x)(x) = 326 Reorder the terms for easier multiplication: x(25 + x) = 326 (25 * x + x * x) = 326 (25x + x2) = 326 Solving 25x + x2 = 326 Solving for variable 'x'. Reorder the terms: -326 + 25x + x2 = 326 + -326 Combine like terms: 326 + -326 = 0 -326 + 25x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '326' to each side of the equation. -326 + 25x + 326 + x2 = 0 + 326 Reorder the terms: -326 + 326 + 25x + x2 = 0 + 326 Combine like terms: -326 + 326 = 0 0 + 25x + x2 = 0 + 326 25x + x2 = 0 + 326 Combine like terms: 0 + 326 = 326 25x + x2 = 326 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 = 326 + 156.25 Reorder the terms: 156.25 + 25x + x2 = 326 + 156.25 Combine like terms: 326 + 156.25 = 482.25 156.25 + 25x + x2 = 482.25 Factor a perfect square on the left side: (x + 12.5)(x + 12.5) = 482.25 Calculate the square root of the right side: 21.960191256 Break this problem into two subproblems by setting (x + 12.5) equal to 21.960191256 and -21.960191256.Subproblem 1
x + 12.5 = 21.960191256 Simplifying x + 12.5 = 21.960191256 Reorder the terms: 12.5 + x = 21.960191256 Solving 12.5 + x = 21.960191256 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 = 21.960191256 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = 21.960191256 + -12.5 x = 21.960191256 + -12.5 Combine like terms: 21.960191256 + -12.5 = 9.460191256 x = 9.460191256 Simplifying x = 9.460191256Subproblem 2
x + 12.5 = -21.960191256 Simplifying x + 12.5 = -21.960191256 Reorder the terms: 12.5 + x = -21.960191256 Solving 12.5 + x = -21.960191256 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 = -21.960191256 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = -21.960191256 + -12.5 x = -21.960191256 + -12.5 Combine like terms: -21.960191256 + -12.5 = -34.460191256 x = -34.460191256 Simplifying x = -34.460191256Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.460191256, -34.460191256}
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