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Simplifying x2 + 20x + -5000 = 0 Reorder the terms: -5000 + 20x + x2 = 0 Solving -5000 + 20x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '5000' to each side of the equation. -5000 + 20x + 5000 + x2 = 0 + 5000 Reorder the terms: -5000 + 5000 + 20x + x2 = 0 + 5000 Combine like terms: -5000 + 5000 = 0 0 + 20x + x2 = 0 + 5000 20x + x2 = 0 + 5000 Combine like terms: 0 + 5000 = 5000 20x + x2 = 5000 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = 5000 + 100 Reorder the terms: 100 + 20x + x2 = 5000 + 100 Combine like terms: 5000 + 100 = 5100 100 + 20x + x2 = 5100 Factor a perfect square on the left side: (x + 10)(x + 10) = 5100 Calculate the square root of the right side: 71.414284285 Break this problem into two subproblems by setting (x + 10) equal to 71.414284285 and -71.414284285.Subproblem 1
x + 10 = 71.414284285 Simplifying x + 10 = 71.414284285 Reorder the terms: 10 + x = 71.414284285 Solving 10 + x = 71.414284285 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 71.414284285 + -10 Combine like terms: 10 + -10 = 0 0 + x = 71.414284285 + -10 x = 71.414284285 + -10 Combine like terms: 71.414284285 + -10 = 61.414284285 x = 61.414284285 Simplifying x = 61.414284285Subproblem 2
x + 10 = -71.414284285 Simplifying x + 10 = -71.414284285 Reorder the terms: 10 + x = -71.414284285 Solving 10 + x = -71.414284285 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -71.414284285 + -10 Combine like terms: 10 + -10 = 0 0 + x = -71.414284285 + -10 x = -71.414284285 + -10 Combine like terms: -71.414284285 + -10 = -81.414284285 x = -81.414284285 Simplifying x = -81.414284285Solution
The solution to the problem is based on the solutions from the subproblems. x = {61.414284285, -81.414284285}
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