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Simplifying x2 + 25x + -525 = 0 Reorder the terms: -525 + 25x + x2 = 0 Solving -525 + 25x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '525' to each side of the equation. -525 + 25x + 525 + x2 = 0 + 525 Reorder the terms: -525 + 525 + 25x + x2 = 0 + 525 Combine like terms: -525 + 525 = 0 0 + 25x + x2 = 0 + 525 25x + x2 = 0 + 525 Combine like terms: 0 + 525 = 525 25x + x2 = 525 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 = 525 + 156.25 Reorder the terms: 156.25 + 25x + x2 = 525 + 156.25 Combine like terms: 525 + 156.25 = 681.25 156.25 + 25x + x2 = 681.25 Factor a perfect square on the left side: (x + 12.5)(x + 12.5) = 681.25 Calculate the square root of the right side: 26.100766272 Break this problem into two subproblems by setting (x + 12.5) equal to 26.100766272 and -26.100766272.Subproblem 1
x + 12.5 = 26.100766272 Simplifying x + 12.5 = 26.100766272 Reorder the terms: 12.5 + x = 26.100766272 Solving 12.5 + x = 26.100766272 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 = 26.100766272 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = 26.100766272 + -12.5 x = 26.100766272 + -12.5 Combine like terms: 26.100766272 + -12.5 = 13.600766272 x = 13.600766272 Simplifying x = 13.600766272Subproblem 2
x + 12.5 = -26.100766272 Simplifying x + 12.5 = -26.100766272 Reorder the terms: 12.5 + x = -26.100766272 Solving 12.5 + x = -26.100766272 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 = -26.100766272 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = -26.100766272 + -12.5 x = -26.100766272 + -12.5 Combine like terms: -26.100766272 + -12.5 = -38.600766272 x = -38.600766272 Simplifying x = -38.600766272Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.600766272, -38.600766272}
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