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Simplifying 9x2 + -127x + 54 = 0 Reorder the terms: 54 + -127x + 9x2 = 0 Solving 54 + -127x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 6 + -14.11111111x + x2 = 0 Move the constant term to the right: Add '-6' to each side of the equation. 6 + -14.11111111x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + -14.11111111x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -14.11111111x + x2 = 0 + -6 -14.11111111x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 -14.11111111x + x2 = -6 The x term is -14.11111111x. Take half its coefficient (-7.055555555). Square it (49.78086419) and add it to both sides. Add '49.78086419' to each side of the equation. -14.11111111x + 49.78086419 + x2 = -6 + 49.78086419 Reorder the terms: 49.78086419 + -14.11111111x + x2 = -6 + 49.78086419 Combine like terms: -6 + 49.78086419 = 43.78086419 49.78086419 + -14.11111111x + x2 = 43.78086419 Factor a perfect square on the left side: (x + -7.055555555)(x + -7.055555555) = 43.78086419 Calculate the square root of the right side: 6.61671098 Break this problem into two subproblems by setting (x + -7.055555555) equal to 6.61671098 and -6.61671098.Subproblem 1
x + -7.055555555 = 6.61671098 Simplifying x + -7.055555555 = 6.61671098 Reorder the terms: -7.055555555 + x = 6.61671098 Solving -7.055555555 + x = 6.61671098 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.055555555' to each side of the equation. -7.055555555 + 7.055555555 + x = 6.61671098 + 7.055555555 Combine like terms: -7.055555555 + 7.055555555 = 0.000000000 0.000000000 + x = 6.61671098 + 7.055555555 x = 6.61671098 + 7.055555555 Combine like terms: 6.61671098 + 7.055555555 = 13.672266535 x = 13.672266535 Simplifying x = 13.672266535Subproblem 2
x + -7.055555555 = -6.61671098 Simplifying x + -7.055555555 = -6.61671098 Reorder the terms: -7.055555555 + x = -6.61671098 Solving -7.055555555 + x = -6.61671098 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.055555555' to each side of the equation. -7.055555555 + 7.055555555 + x = -6.61671098 + 7.055555555 Combine like terms: -7.055555555 + 7.055555555 = 0.000000000 0.000000000 + x = -6.61671098 + 7.055555555 x = -6.61671098 + 7.055555555 Combine like terms: -6.61671098 + 7.055555555 = 0.438844575 x = 0.438844575 Simplifying x = 0.438844575Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.672266535, 0.438844575}
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