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Simplifying x2 + 25x + -46 = 0 Reorder the terms: -46 + 25x + x2 = 0 Solving -46 + 25x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '46' to each side of the equation. -46 + 25x + 46 + x2 = 0 + 46 Reorder the terms: -46 + 46 + 25x + x2 = 0 + 46 Combine like terms: -46 + 46 = 0 0 + 25x + x2 = 0 + 46 25x + x2 = 0 + 46 Combine like terms: 0 + 46 = 46 25x + x2 = 46 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 = 46 + 156.25 Reorder the terms: 156.25 + 25x + x2 = 46 + 156.25 Combine like terms: 46 + 156.25 = 202.25 156.25 + 25x + x2 = 202.25 Factor a perfect square on the left side: (x + 12.5)(x + 12.5) = 202.25 Calculate the square root of the right side: 14.221462653 Break this problem into two subproblems by setting (x + 12.5) equal to 14.221462653 and -14.221462653.Subproblem 1
x + 12.5 = 14.221462653 Simplifying x + 12.5 = 14.221462653 Reorder the terms: 12.5 + x = 14.221462653 Solving 12.5 + x = 14.221462653 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 = 14.221462653 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = 14.221462653 + -12.5 x = 14.221462653 + -12.5 Combine like terms: 14.221462653 + -12.5 = 1.721462653 x = 1.721462653 Simplifying x = 1.721462653Subproblem 2
x + 12.5 = -14.221462653 Simplifying x + 12.5 = -14.221462653 Reorder the terms: 12.5 + x = -14.221462653 Solving 12.5 + x = -14.221462653 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 = -14.221462653 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = -14.221462653 + -12.5 x = -14.221462653 + -12.5 Combine like terms: -14.221462653 + -12.5 = -26.721462653 x = -26.721462653 Simplifying x = -26.721462653Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.721462653, -26.721462653}
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