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Simplifying x2 + 25x + -1050 = 0 Reorder the terms: -1050 + 25x + x2 = 0 Solving -1050 + 25x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1050' to each side of the equation. -1050 + 25x + 1050 + x2 = 0 + 1050 Reorder the terms: -1050 + 1050 + 25x + x2 = 0 + 1050 Combine like terms: -1050 + 1050 = 0 0 + 25x + x2 = 0 + 1050 25x + x2 = 0 + 1050 Combine like terms: 0 + 1050 = 1050 25x + x2 = 1050 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 = 1050 + 156.25 Reorder the terms: 156.25 + 25x + x2 = 1050 + 156.25 Combine like terms: 1050 + 156.25 = 1206.25 156.25 + 25x + x2 = 1206.25 Factor a perfect square on the left side: (x + 12.5)(x + 12.5) = 1206.25 Calculate the square root of the right side: 34.731109974 Break this problem into two subproblems by setting (x + 12.5) equal to 34.731109974 and -34.731109974.Subproblem 1
x + 12.5 = 34.731109974 Simplifying x + 12.5 = 34.731109974 Reorder the terms: 12.5 + x = 34.731109974 Solving 12.5 + x = 34.731109974 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 = 34.731109974 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = 34.731109974 + -12.5 x = 34.731109974 + -12.5 Combine like terms: 34.731109974 + -12.5 = 22.231109974 x = 22.231109974 Simplifying x = 22.231109974Subproblem 2
x + 12.5 = -34.731109974 Simplifying x + 12.5 = -34.731109974 Reorder the terms: 12.5 + x = -34.731109974 Solving 12.5 + x = -34.731109974 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 = -34.731109974 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = -34.731109974 + -12.5 x = -34.731109974 + -12.5 Combine like terms: -34.731109974 + -12.5 = -47.231109974 x = -47.231109974 Simplifying x = -47.231109974Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.231109974, -47.231109974}
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