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Simplifying 2500 = 25x + x2 Solving 2500 = 25x + x2 Solving for variable 'x'. Reorder the terms: 2500 + -25x + -1x2 = 25x + -25x + x2 + -1x2 Combine like terms: 25x + -25x = 0 2500 + -25x + -1x2 = 0 + x2 + -1x2 2500 + -25x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 2500 + -25x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -2500 + 25x + x2 = 0 Move the constant term to the right: Add '2500' to each side of the equation. -2500 + 25x + 2500 + x2 = 0 + 2500 Reorder the terms: -2500 + 2500 + 25x + x2 = 0 + 2500 Combine like terms: -2500 + 2500 = 0 0 + 25x + x2 = 0 + 2500 25x + x2 = 0 + 2500 Combine like terms: 0 + 2500 = 2500 25x + x2 = 2500 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 = 2500 + 156.25 Reorder the terms: 156.25 + 25x + x2 = 2500 + 156.25 Combine like terms: 2500 + 156.25 = 2656.25 156.25 + 25x + x2 = 2656.25 Factor a perfect square on the left side: (x + 12.5)(x + 12.5) = 2656.25 Calculate the square root of the right side: 51.53882032 Break this problem into two subproblems by setting (x + 12.5) equal to 51.53882032 and -51.53882032.Subproblem 1
x + 12.5 = 51.53882032 Simplifying x + 12.5 = 51.53882032 Reorder the terms: 12.5 + x = 51.53882032 Solving 12.5 + x = 51.53882032 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 = 51.53882032 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = 51.53882032 + -12.5 x = 51.53882032 + -12.5 Combine like terms: 51.53882032 + -12.5 = 39.03882032 x = 39.03882032 Simplifying x = 39.03882032Subproblem 2
x + 12.5 = -51.53882032 Simplifying x + 12.5 = -51.53882032 Reorder the terms: 12.5 + x = -51.53882032 Solving 12.5 + x = -51.53882032 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 = -51.53882032 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = -51.53882032 + -12.5 x = -51.53882032 + -12.5 Combine like terms: -51.53882032 + -12.5 = -64.03882032 x = -64.03882032 Simplifying x = -64.03882032Solution
The solution to the problem is based on the solutions from the subproblems. x = {39.03882032, -64.03882032}
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