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Simplifying 9x2 + -127x + 386 = 0 Reorder the terms: 386 + -127x + 9x2 = 0 Solving 386 + -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'. 42.88888889 + -14.11111111x + x2 = 0 Move the constant term to the right: Add '-42.88888889' to each side of the equation. 42.88888889 + -14.11111111x + -42.88888889 + x2 = 0 + -42.88888889 Reorder the terms: 42.88888889 + -42.88888889 + -14.11111111x + x2 = 0 + -42.88888889 Combine like terms: 42.88888889 + -42.88888889 = 0.00000000 0.00000000 + -14.11111111x + x2 = 0 + -42.88888889 -14.11111111x + x2 = 0 + -42.88888889 Combine like terms: 0 + -42.88888889 = -42.88888889 -14.11111111x + x2 = -42.88888889 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 = -42.88888889 + 49.78086419 Reorder the terms: 49.78086419 + -14.11111111x + x2 = -42.88888889 + 49.78086419 Combine like terms: -42.88888889 + 49.78086419 = 6.8919753 49.78086419 + -14.11111111x + x2 = 6.8919753 Factor a perfect square on the left side: (x + -7.055555555)(x + -7.055555555) = 6.8919753 Calculate the square root of the right side: 2.625257187 Break this problem into two subproblems by setting (x + -7.055555555) equal to 2.625257187 and -2.625257187.Subproblem 1
x + -7.055555555 = 2.625257187 Simplifying x + -7.055555555 = 2.625257187 Reorder the terms: -7.055555555 + x = 2.625257187 Solving -7.055555555 + x = 2.625257187 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 = 2.625257187 + 7.055555555 Combine like terms: -7.055555555 + 7.055555555 = 0.000000000 0.000000000 + x = 2.625257187 + 7.055555555 x = 2.625257187 + 7.055555555 Combine like terms: 2.625257187 + 7.055555555 = 9.680812742 x = 9.680812742 Simplifying x = 9.680812742Subproblem 2
x + -7.055555555 = -2.625257187 Simplifying x + -7.055555555 = -2.625257187 Reorder the terms: -7.055555555 + x = -2.625257187 Solving -7.055555555 + x = -2.625257187 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 = -2.625257187 + 7.055555555 Combine like terms: -7.055555555 + 7.055555555 = 0.000000000 0.000000000 + x = -2.625257187 + 7.055555555 x = -2.625257187 + 7.055555555 Combine like terms: -2.625257187 + 7.055555555 = 4.430298368 x = 4.430298368 Simplifying x = 4.430298368Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.680812742, 4.430298368}
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