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Simplifying x2 + 25x + -20000 = 0 Reorder the terms: -20000 + 25x + x2 = 0 Solving -20000 + 25x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '20000' to each side of the equation. -20000 + 25x + 20000 + x2 = 0 + 20000 Reorder the terms: -20000 + 20000 + 25x + x2 = 0 + 20000 Combine like terms: -20000 + 20000 = 0 0 + 25x + x2 = 0 + 20000 25x + x2 = 0 + 20000 Combine like terms: 0 + 20000 = 20000 25x + x2 = 20000 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 = 20000 + 156.25 Reorder the terms: 156.25 + 25x + x2 = 20000 + 156.25 Combine like terms: 20000 + 156.25 = 20156.25 156.25 + 25x + x2 = 20156.25 Factor a perfect square on the left side: (x + 12.5)(x + 12.5) = 20156.25 Calculate the square root of the right side: 141.972708645 Break this problem into two subproblems by setting (x + 12.5) equal to 141.972708645 and -141.972708645.Subproblem 1
x + 12.5 = 141.972708645 Simplifying x + 12.5 = 141.972708645 Reorder the terms: 12.5 + x = 141.972708645 Solving 12.5 + x = 141.972708645 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 = 141.972708645 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = 141.972708645 + -12.5 x = 141.972708645 + -12.5 Combine like terms: 141.972708645 + -12.5 = 129.472708645 x = 129.472708645 Simplifying x = 129.472708645Subproblem 2
x + 12.5 = -141.972708645 Simplifying x + 12.5 = -141.972708645 Reorder the terms: 12.5 + x = -141.972708645 Solving 12.5 + x = -141.972708645 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 = -141.972708645 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = -141.972708645 + -12.5 x = -141.972708645 + -12.5 Combine like terms: -141.972708645 + -12.5 = -154.472708645 x = -154.472708645 Simplifying x = -154.472708645Solution
The solution to the problem is based on the solutions from the subproblems. x = {129.472708645, -154.472708645}
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