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Simplifying 9x2 + -1x + -10000 = 0 Reorder the terms: -10000 + -1x + 9x2 = 0 Solving -10000 + -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'. -1111.111111 + -0.1111111111x + x2 = 0 Move the constant term to the right: Add '1111.111111' to each side of the equation. -1111.111111 + -0.1111111111x + 1111.111111 + x2 = 0 + 1111.111111 Reorder the terms: -1111.111111 + 1111.111111 + -0.1111111111x + x2 = 0 + 1111.111111 Combine like terms: -1111.111111 + 1111.111111 = 0.000000 0.000000 + -0.1111111111x + x2 = 0 + 1111.111111 -0.1111111111x + x2 = 0 + 1111.111111 Combine like terms: 0 + 1111.111111 = 1111.111111 -0.1111111111x + x2 = 1111.111111 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 = 1111.111111 + 0.003086419752 Reorder the terms: 0.003086419752 + -0.1111111111x + x2 = 1111.111111 + 0.003086419752 Combine like terms: 1111.111111 + 0.003086419752 = 1111.114197419752 0.003086419752 + -0.1111111111x + x2 = 1111.114197419752 Factor a perfect square on the left side: (x + -0.05555555555)(x + -0.05555555555) = 1111.114197419752 Calculate the square root of the right side: 33.333379628 Break this problem into two subproblems by setting (x + -0.05555555555) equal to 33.333379628 and -33.333379628.Subproblem 1
x + -0.05555555555 = 33.333379628 Simplifying x + -0.05555555555 = 33.333379628 Reorder the terms: -0.05555555555 + x = 33.333379628 Solving -0.05555555555 + x = 33.333379628 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 = 33.333379628 + 0.05555555555 Combine like terms: -0.05555555555 + 0.05555555555 = 0.00000000000 0.00000000000 + x = 33.333379628 + 0.05555555555 x = 33.333379628 + 0.05555555555 Combine like terms: 33.333379628 + 0.05555555555 = 33.38893518355 x = 33.38893518355 Simplifying x = 33.38893518355Subproblem 2
x + -0.05555555555 = -33.333379628 Simplifying x + -0.05555555555 = -33.333379628 Reorder the terms: -0.05555555555 + x = -33.333379628 Solving -0.05555555555 + x = -33.333379628 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 = -33.333379628 + 0.05555555555 Combine like terms: -0.05555555555 + 0.05555555555 = 0.00000000000 0.00000000000 + x = -33.333379628 + 0.05555555555 x = -33.333379628 + 0.05555555555 Combine like terms: -33.333379628 + 0.05555555555 = -33.27782407245 x = -33.27782407245 Simplifying x = -33.27782407245Solution
The solution to the problem is based on the solutions from the subproblems. x = {33.38893518355, -33.27782407245}
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