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Simplifying 9x(9x + -1) = 1 Reorder the terms: 9x(-1 + 9x) = 1 (-1 * 9x + 9x * 9x) = 1 (-9x + 81x2) = 1 Solving -9x + 81x2 = 1 Solving for variable 'x'. Reorder the terms: -1 + -9x + 81x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + -9x + 81x2 = 0 Begin completing the square. Divide all terms by 81 the coefficient of the squared term: Divide each side by '81'. -0.01234567901 + -0.1111111111x + x2 = 0 Move the constant term to the right: Add '0.01234567901' to each side of the equation. -0.01234567901 + -0.1111111111x + 0.01234567901 + x2 = 0 + 0.01234567901 Reorder the terms: -0.01234567901 + 0.01234567901 + -0.1111111111x + x2 = 0 + 0.01234567901 Combine like terms: -0.01234567901 + 0.01234567901 = 0.00000000000 0.00000000000 + -0.1111111111x + x2 = 0 + 0.01234567901 -0.1111111111x + x2 = 0 + 0.01234567901 Combine like terms: 0 + 0.01234567901 = 0.01234567901 -0.1111111111x + x2 = 0.01234567901 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 = 0.01234567901 + 0.003086419752 Reorder the terms: 0.003086419752 + -0.1111111111x + x2 = 0.01234567901 + 0.003086419752 Combine like terms: 0.01234567901 + 0.003086419752 = 0.015432098762 0.003086419752 + -0.1111111111x + x2 = 0.015432098762 Factor a perfect square on the left side: (x + -0.05555555555)(x + -0.05555555555) = 0.015432098762 Calculate the square root of the right side: 0.124225999 Break this problem into two subproblems by setting (x + -0.05555555555) equal to 0.124225999 and -0.124225999.Subproblem 1
x + -0.05555555555 = 0.124225999 Simplifying x + -0.05555555555 = 0.124225999 Reorder the terms: -0.05555555555 + x = 0.124225999 Solving -0.05555555555 + x = 0.124225999 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 = 0.124225999 + 0.05555555555 Combine like terms: -0.05555555555 + 0.05555555555 = 0.00000000000 0.00000000000 + x = 0.124225999 + 0.05555555555 x = 0.124225999 + 0.05555555555 Combine like terms: 0.124225999 + 0.05555555555 = 0.17978155455 x = 0.17978155455 Simplifying x = 0.17978155455Subproblem 2
x + -0.05555555555 = -0.124225999 Simplifying x + -0.05555555555 = -0.124225999 Reorder the terms: -0.05555555555 + x = -0.124225999 Solving -0.05555555555 + x = -0.124225999 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 = -0.124225999 + 0.05555555555 Combine like terms: -0.05555555555 + 0.05555555555 = 0.00000000000 0.00000000000 + x = -0.124225999 + 0.05555555555 x = -0.124225999 + 0.05555555555 Combine like terms: -0.124225999 + 0.05555555555 = -0.06867044345 x = -0.06867044345 Simplifying x = -0.06867044345Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.17978155455, -0.06867044345}
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