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Simplifying x(x + 25) = 323 Reorder the terms: x(25 + x) = 323 (25 * x + x * x) = 323 (25x + x2) = 323 Solving 25x + x2 = 323 Solving for variable 'x'. Reorder the terms: -323 + 25x + x2 = 323 + -323 Combine like terms: 323 + -323 = 0 -323 + 25x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '323' to each side of the equation. -323 + 25x + 323 + x2 = 0 + 323 Reorder the terms: -323 + 323 + 25x + x2 = 0 + 323 Combine like terms: -323 + 323 = 0 0 + 25x + x2 = 0 + 323 25x + x2 = 0 + 323 Combine like terms: 0 + 323 = 323 25x + x2 = 323 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 = 323 + 156.25 Reorder the terms: 156.25 + 25x + x2 = 323 + 156.25 Combine like terms: 323 + 156.25 = 479.25 156.25 + 25x + x2 = 479.25 Factor a perfect square on the left side: (x + 12.5)(x + 12.5) = 479.25 Calculate the square root of the right side: 21.891779279 Break this problem into two subproblems by setting (x + 12.5) equal to 21.891779279 and -21.891779279.Subproblem 1
x + 12.5 = 21.891779279 Simplifying x + 12.5 = 21.891779279 Reorder the terms: 12.5 + x = 21.891779279 Solving 12.5 + x = 21.891779279 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 = 21.891779279 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = 21.891779279 + -12.5 x = 21.891779279 + -12.5 Combine like terms: 21.891779279 + -12.5 = 9.391779279 x = 9.391779279 Simplifying x = 9.391779279Subproblem 2
x + 12.5 = -21.891779279 Simplifying x + 12.5 = -21.891779279 Reorder the terms: 12.5 + x = -21.891779279 Solving 12.5 + x = -21.891779279 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 = -21.891779279 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = -21.891779279 + -12.5 x = -21.891779279 + -12.5 Combine like terms: -21.891779279 + -12.5 = -34.391779279 x = -34.391779279 Simplifying x = -34.391779279Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.391779279, -34.391779279}
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