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Simplifying 625 = 0.5x(25 + x) 625 = (25 * 0.5x + x * 0.5x) 625 = (12.5x + 0.5x2) Solving 625 = 12.5x + 0.5x2 Solving for variable 'x'. Reorder the terms: 625 + -12.5x + -0.5x2 = 12.5x + -12.5x + 0.5x2 + -0.5x2 Combine like terms: 12.5x + -12.5x = 0.0 625 + -12.5x + -0.5x2 = 0.0 + 0.5x2 + -0.5x2 625 + -12.5x + -0.5x2 = 0.5x2 + -0.5x2 Combine like terms: 0.5x2 + -0.5x2 = 0.0 625 + -12.5x + -0.5x2 = 0.0 Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. -1250 + 25x + x2 = 0 Move the constant term to the right: Add '1250' to each side of the equation. -1250 + 25x + 1250 + x2 = 0 + 1250 Reorder the terms: -1250 + 1250 + 25x + x2 = 0 + 1250 Combine like terms: -1250 + 1250 = 0 0 + 25x + x2 = 0 + 1250 25x + x2 = 0 + 1250 Combine like terms: 0 + 1250 = 1250 25x + x2 = 1250 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 = 1250 + 156.25 Reorder the terms: 156.25 + 25x + x2 = 1250 + 156.25 Combine like terms: 1250 + 156.25 = 1406.25 156.25 + 25x + x2 = 1406.25 Factor a perfect square on the left side: (x + 12.5)(x + 12.5) = 1406.25 Calculate the square root of the right side: 37.5 Break this problem into two subproblems by setting (x + 12.5) equal to 37.5 and -37.5.Subproblem 1
x + 12.5 = 37.5 Simplifying x + 12.5 = 37.5 Reorder the terms: 12.5 + x = 37.5 Solving 12.5 + x = 37.5 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 = 37.5 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = 37.5 + -12.5 x = 37.5 + -12.5 Combine like terms: 37.5 + -12.5 = 25 x = 25 Simplifying x = 25Subproblem 2
x + 12.5 = -37.5 Simplifying x + 12.5 = -37.5 Reorder the terms: 12.5 + x = -37.5 Solving 12.5 + x = -37.5 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 = -37.5 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = -37.5 + -12.5 x = -37.5 + -12.5 Combine like terms: -37.5 + -12.5 = -50 x = -50 Simplifying x = -50Solution
The solution to the problem is based on the solutions from the subproblems. x = {25, -50}
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