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Simplifying -9x2 + 1x + 3 = 0 Reorder the terms: 3 + 1x + -9x2 = 0 Solving 3 + 1x + -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'. -0.3333333333 + -0.1111111111x + x2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + -0.1111111111x + 0.3333333333 + x2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + -0.1111111111x + x2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + -0.1111111111x + x2 = 0 + 0.3333333333 -0.1111111111x + x2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 -0.1111111111x + x2 = 0.3333333333 The x term is -0.1111111111x. Take half its coefficient (-0.05555555555). Square it (0.003086419752) and add it to both sides. Add '0.003086419752' to each side of the equation. -0.1111111111x + 0.003086419752 + x2 = 0.3333333333 + 0.003086419752 Reorder the terms: 0.003086419752 + -0.1111111111x + x2 = 0.3333333333 + 0.003086419752 Combine like terms: 0.3333333333 + 0.003086419752 = 0.336419753052 0.003086419752 + -0.1111111111x + x2 = 0.336419753052 Factor a perfect square on the left side: (x + -0.05555555555)(x + -0.05555555555) = 0.336419753052 Calculate the square root of the right side: 0.580017028 Break this problem into two subproblems by setting (x + -0.05555555555) equal to 0.580017028 and -0.580017028.Subproblem 1
x + -0.05555555555 = 0.580017028 Simplifying x + -0.05555555555 = 0.580017028 Reorder the terms: -0.05555555555 + x = 0.580017028 Solving -0.05555555555 + x = 0.580017028 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.05555555555' to each side of the equation. -0.05555555555 + 0.05555555555 + x = 0.580017028 + 0.05555555555 Combine like terms: -0.05555555555 + 0.05555555555 = 0.00000000000 0.00000000000 + x = 0.580017028 + 0.05555555555 x = 0.580017028 + 0.05555555555 Combine like terms: 0.580017028 + 0.05555555555 = 0.63557258355 x = 0.63557258355 Simplifying x = 0.63557258355Subproblem 2
x + -0.05555555555 = -0.580017028 Simplifying x + -0.05555555555 = -0.580017028 Reorder the terms: -0.05555555555 + x = -0.580017028 Solving -0.05555555555 + x = -0.580017028 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.05555555555' to each side of the equation. -0.05555555555 + 0.05555555555 + x = -0.580017028 + 0.05555555555 Combine like terms: -0.05555555555 + 0.05555555555 = 0.00000000000 0.00000000000 + x = -0.580017028 + 0.05555555555 x = -0.580017028 + 0.05555555555 Combine like terms: -0.580017028 + 0.05555555555 = -0.52446147245 x = -0.52446147245 Simplifying x = -0.52446147245Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.63557258355, -0.52446147245}
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