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Simplifying x2 + -25x + 27 = 0 Reorder the terms: 27 + -25x + x2 = 0 Solving 27 + -25x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-27' to each side of the equation. 27 + -25x + -27 + x2 = 0 + -27 Reorder the terms: 27 + -27 + -25x + x2 = 0 + -27 Combine like terms: 27 + -27 = 0 0 + -25x + x2 = 0 + -27 -25x + x2 = 0 + -27 Combine like terms: 0 + -27 = -27 -25x + x2 = -27 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 = -27 + 156.25 Reorder the terms: 156.25 + -25x + x2 = -27 + 156.25 Combine like terms: -27 + 156.25 = 129.25 156.25 + -25x + x2 = 129.25 Factor a perfect square on the left side: (x + -12.5)(x + -12.5) = 129.25 Calculate the square root of the right side: 11.368817001 Break this problem into two subproblems by setting (x + -12.5) equal to 11.368817001 and -11.368817001.Subproblem 1
x + -12.5 = 11.368817001 Simplifying x + -12.5 = 11.368817001 Reorder the terms: -12.5 + x = 11.368817001 Solving -12.5 + x = 11.368817001 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 = 11.368817001 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = 11.368817001 + 12.5 x = 11.368817001 + 12.5 Combine like terms: 11.368817001 + 12.5 = 23.868817001 x = 23.868817001 Simplifying x = 23.868817001Subproblem 2
x + -12.5 = -11.368817001 Simplifying x + -12.5 = -11.368817001 Reorder the terms: -12.5 + x = -11.368817001 Solving -12.5 + x = -11.368817001 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 = -11.368817001 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = -11.368817001 + 12.5 x = -11.368817001 + 12.5 Combine like terms: -11.368817001 + 12.5 = 1.131182999 x = 1.131182999 Simplifying x = 1.131182999Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.868817001, 1.131182999}
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