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Simplifying x2 + 25x + -100 = 0 Reorder the terms: -100 + 25x + x2 = 0 Solving -100 + 25x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '100' to each side of the equation. -100 + 25x + 100 + x2 = 0 + 100 Reorder the terms: -100 + 100 + 25x + x2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + 25x + x2 = 0 + 100 25x + x2 = 0 + 100 Combine like terms: 0 + 100 = 100 25x + x2 = 100 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 = 100 + 156.25 Reorder the terms: 156.25 + 25x + x2 = 100 + 156.25 Combine like terms: 100 + 156.25 = 256.25 156.25 + 25x + x2 = 256.25 Factor a perfect square on the left side: (x + 12.5)(x + 12.5) = 256.25 Calculate the square root of the right side: 16.007810594 Break this problem into two subproblems by setting (x + 12.5) equal to 16.007810594 and -16.007810594.Subproblem 1
x + 12.5 = 16.007810594 Simplifying x + 12.5 = 16.007810594 Reorder the terms: 12.5 + x = 16.007810594 Solving 12.5 + x = 16.007810594 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 = 16.007810594 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = 16.007810594 + -12.5 x = 16.007810594 + -12.5 Combine like terms: 16.007810594 + -12.5 = 3.507810594 x = 3.507810594 Simplifying x = 3.507810594Subproblem 2
x + 12.5 = -16.007810594 Simplifying x + 12.5 = -16.007810594 Reorder the terms: 12.5 + x = -16.007810594 Solving 12.5 + x = -16.007810594 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 = -16.007810594 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = -16.007810594 + -12.5 x = -16.007810594 + -12.5 Combine like terms: -16.007810594 + -12.5 = -28.507810594 x = -28.507810594 Simplifying x = -28.507810594Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.507810594, -28.507810594}
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