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Simplifying 9x2 + -15x + 14x + -9 = 0 Reorder the terms: -9 + -15x + 14x + 9x2 = 0 Combine like terms: -15x + 14x = -1x -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 = 1.05709757655 x = 1.05709757655 Simplifying x = 1.05709757655Subproblem 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 = -0.94598646545 x = -0.94598646545 Simplifying x = -0.94598646545Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.05709757655, -0.94598646545}
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