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Simplifying -9x2 + -1x + 9 = 0 Reorder the terms: 9 + -1x + -9x2 = 0 Solving 9 + -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'. -1 + 0.1111111111x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 0.1111111111x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 0.1111111111x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 0.1111111111x + x2 = 0 + 1 0.1111111111x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 0.1111111111x + x2 = 1 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 = 1 + 0.003086419752 Reorder the terms: 0.003086419752 + 0.1111111111x + x2 = 1 + 0.003086419752 Combine like terms: 1 + 0.003086419752 = 1.003086419752 0.003086419752 + 0.1111111111x + x2 = 1.003086419752 Factor a perfect square on the left side: (x + 0.05555555555)(x + 0.05555555555) = 1.003086419752 Calculate the square root of the right side: 1.001542021 Break this problem into two subproblems by setting (x + 0.05555555555) equal to 1.001542021 and -1.001542021.Subproblem 1
x + 0.05555555555 = 1.001542021 Simplifying x + 0.05555555555 = 1.001542021 Reorder the terms: 0.05555555555 + x = 1.001542021 Solving 0.05555555555 + x = 1.001542021 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 = 1.001542021 + -0.05555555555 Combine like terms: 0.05555555555 + -0.05555555555 = 0.00000000000 0.00000000000 + x = 1.001542021 + -0.05555555555 x = 1.001542021 + -0.05555555555 Combine like terms: 1.001542021 + -0.05555555555 = 0.94598646545 x = 0.94598646545 Simplifying x = 0.94598646545Subproblem 2
x + 0.05555555555 = -1.001542021 Simplifying x + 0.05555555555 = -1.001542021 Reorder the terms: 0.05555555555 + x = -1.001542021 Solving 0.05555555555 + x = -1.001542021 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 = -1.001542021 + -0.05555555555 Combine like terms: 0.05555555555 + -0.05555555555 = 0.00000000000 0.00000000000 + x = -1.001542021 + -0.05555555555 x = -1.001542021 + -0.05555555555 Combine like terms: -1.001542021 + -0.05555555555 = -1.05709757655 x = -1.05709757655 Simplifying x = -1.05709757655Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.94598646545, -1.05709757655}
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