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Simplifying x2 + -25x + 85 = 0 Reorder the terms: 85 + -25x + x2 = 0 Solving 85 + -25x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-85' to each side of the equation. 85 + -25x + -85 + x2 = 0 + -85 Reorder the terms: 85 + -85 + -25x + x2 = 0 + -85 Combine like terms: 85 + -85 = 0 0 + -25x + x2 = 0 + -85 -25x + x2 = 0 + -85 Combine like terms: 0 + -85 = -85 -25x + x2 = -85 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 = -85 + 156.25 Reorder the terms: 156.25 + -25x + x2 = -85 + 156.25 Combine like terms: -85 + 156.25 = 71.25 156.25 + -25x + x2 = 71.25 Factor a perfect square on the left side: (x + -12.5)(x + -12.5) = 71.25 Calculate the square root of the right side: 8.440971508 Break this problem into two subproblems by setting (x + -12.5) equal to 8.440971508 and -8.440971508.Subproblem 1
x + -12.5 = 8.440971508 Simplifying x + -12.5 = 8.440971508 Reorder the terms: -12.5 + x = 8.440971508 Solving -12.5 + x = 8.440971508 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 = 8.440971508 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = 8.440971508 + 12.5 x = 8.440971508 + 12.5 Combine like terms: 8.440971508 + 12.5 = 20.940971508 x = 20.940971508 Simplifying x = 20.940971508Subproblem 2
x + -12.5 = -8.440971508 Simplifying x + -12.5 = -8.440971508 Reorder the terms: -12.5 + x = -8.440971508 Solving -12.5 + x = -8.440971508 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 = -8.440971508 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = -8.440971508 + 12.5 x = -8.440971508 + 12.5 Combine like terms: -8.440971508 + 12.5 = 4.059028492 x = 4.059028492 Simplifying x = 4.059028492Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.940971508, 4.059028492}
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