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Simplifying 0.9x2 + -0.1x + -1 = 0 Reorder the terms: -1 + -0.1x + 0.9x2 = 0 Solving -1 + -0.1x + 0.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.9 the coefficient of the squared term: Divide each side by '0.9'. -1.111111111 + -0.1111111111x + x2 = 0 Move the constant term to the right: Add '1.111111111' to each side of the equation. -1.111111111 + -0.1111111111x + 1.111111111 + x2 = 0 + 1.111111111 Reorder the terms: -1.111111111 + 1.111111111 + -0.1111111111x + x2 = 0 + 1.111111111 Combine like terms: -1.111111111 + 1.111111111 = 0.000000000 0.000000000 + -0.1111111111x + x2 = 0 + 1.111111111 -0.1111111111x + x2 = 0 + 1.111111111 Combine like terms: 0 + 1.111111111 = 1.111111111 -0.1111111111x + x2 = 1.111111111 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 = 1.111111111 + 0.003086419752 Reorder the terms: 0.003086419752 + -0.1111111111x + x2 = 1.111111111 + 0.003086419752 Combine like terms: 1.111111111 + 0.003086419752 = 1.114197530752 0.003086419752 + -0.1111111111x + x2 = 1.114197530752 Factor a perfect square on the left side: (x + -0.05555555555)(x + -0.05555555555) = 1.114197530752 Calculate the square root of the right side: 1.055555556 Break this problem into two subproblems by setting (x + -0.05555555555) equal to 1.055555556 and -1.055555556.Subproblem 1
x + -0.05555555555 = 1.055555556 Simplifying x + -0.05555555555 = 1.055555556 Reorder the terms: -0.05555555555 + x = 1.055555556 Solving -0.05555555555 + x = 1.055555556 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 = 1.055555556 + 0.05555555555 Combine like terms: -0.05555555555 + 0.05555555555 = 0.00000000000 0.00000000000 + x = 1.055555556 + 0.05555555555 x = 1.055555556 + 0.05555555555 Combine like terms: 1.055555556 + 0.05555555555 = 1.11111111155 x = 1.11111111155 Simplifying x = 1.11111111155Subproblem 2
x + -0.05555555555 = -1.055555556 Simplifying x + -0.05555555555 = -1.055555556 Reorder the terms: -0.05555555555 + x = -1.055555556 Solving -0.05555555555 + x = -1.055555556 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 = -1.055555556 + 0.05555555555 Combine like terms: -0.05555555555 + 0.05555555555 = 0.00000000000 0.00000000000 + x = -1.055555556 + 0.05555555555 x = -1.055555556 + 0.05555555555 Combine like terms: -1.055555556 + 0.05555555555 = -1.00000000045 x = -1.00000000045 Simplifying x = -1.00000000045Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.11111111155, -1.00000000045}
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