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Simplifying x2 + -25x + -440 = 0 Reorder the terms: -440 + -25x + x2 = 0 Solving -440 + -25x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '440' to each side of the equation. -440 + -25x + 440 + x2 = 0 + 440 Reorder the terms: -440 + 440 + -25x + x2 = 0 + 440 Combine like terms: -440 + 440 = 0 0 + -25x + x2 = 0 + 440 -25x + x2 = 0 + 440 Combine like terms: 0 + 440 = 440 -25x + x2 = 440 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 = 440 + 156.25 Reorder the terms: 156.25 + -25x + x2 = 440 + 156.25 Combine like terms: 440 + 156.25 = 596.25 156.25 + -25x + x2 = 596.25 Factor a perfect square on the left side: (x + -12.5)(x + -12.5) = 596.25 Calculate the square root of the right side: 24.418230894 Break this problem into two subproblems by setting (x + -12.5) equal to 24.418230894 and -24.418230894.Subproblem 1
x + -12.5 = 24.418230894 Simplifying x + -12.5 = 24.418230894 Reorder the terms: -12.5 + x = 24.418230894 Solving -12.5 + x = 24.418230894 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 = 24.418230894 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = 24.418230894 + 12.5 x = 24.418230894 + 12.5 Combine like terms: 24.418230894 + 12.5 = 36.918230894 x = 36.918230894 Simplifying x = 36.918230894Subproblem 2
x + -12.5 = -24.418230894 Simplifying x + -12.5 = -24.418230894 Reorder the terms: -12.5 + x = -24.418230894 Solving -12.5 + x = -24.418230894 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 = -24.418230894 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = -24.418230894 + 12.5 x = -24.418230894 + 12.5 Combine like terms: -24.418230894 + 12.5 = -11.918230894 x = -11.918230894 Simplifying x = -11.918230894Solution
The solution to the problem is based on the solutions from the subproblems. x = {36.918230894, -11.918230894}
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