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Simplifying x2 + 3x + -127 = 0 Reorder the terms: -127 + 3x + x2 = 0 Solving -127 + 3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '127' to each side of the equation. -127 + 3x + 127 + x2 = 0 + 127 Reorder the terms: -127 + 127 + 3x + x2 = 0 + 127 Combine like terms: -127 + 127 = 0 0 + 3x + x2 = 0 + 127 3x + x2 = 0 + 127 Combine like terms: 0 + 127 = 127 3x + x2 = 127 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 127 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 127 + 2.25 Combine like terms: 127 + 2.25 = 129.25 2.25 + 3x + x2 = 129.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 129.25 Calculate the square root of the right side: 11.368817001 Break this problem into two subproblems by setting (x + 1.5) equal to 11.368817001 and -11.368817001.Subproblem 1
x + 1.5 = 11.368817001 Simplifying x + 1.5 = 11.368817001 Reorder the terms: 1.5 + x = 11.368817001 Solving 1.5 + x = 11.368817001 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 11.368817001 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 11.368817001 + -1.5 x = 11.368817001 + -1.5 Combine like terms: 11.368817001 + -1.5 = 9.868817001 x = 9.868817001 Simplifying x = 9.868817001Subproblem 2
x + 1.5 = -11.368817001 Simplifying x + 1.5 = -11.368817001 Reorder the terms: 1.5 + x = -11.368817001 Solving 1.5 + x = -11.368817001 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -11.368817001 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -11.368817001 + -1.5 x = -11.368817001 + -1.5 Combine like terms: -11.368817001 + -1.5 = -12.868817001 x = -12.868817001 Simplifying x = -12.868817001Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.868817001, -12.868817001}
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