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Simplifying 81x2 + 9x + -1012 = 0 Reorder the terms: -1012 + 9x + 81x2 = 0 Solving -1012 + 9x + 81x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 81 the coefficient of the squared term: Divide each side by '81'. -12.49382716 + 0.1111111111x + x2 = 0 Move the constant term to the right: Add '12.49382716' to each side of the equation. -12.49382716 + 0.1111111111x + 12.49382716 + x2 = 0 + 12.49382716 Reorder the terms: -12.49382716 + 12.49382716 + 0.1111111111x + x2 = 0 + 12.49382716 Combine like terms: -12.49382716 + 12.49382716 = 0.00000000 0.00000000 + 0.1111111111x + x2 = 0 + 12.49382716 0.1111111111x + x2 = 0 + 12.49382716 Combine like terms: 0 + 12.49382716 = 12.49382716 0.1111111111x + x2 = 12.49382716 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 = 12.49382716 + 0.003086419752 Reorder the terms: 0.003086419752 + 0.1111111111x + x2 = 12.49382716 + 0.003086419752 Combine like terms: 12.49382716 + 0.003086419752 = 12.496913579752 0.003086419752 + 0.1111111111x + x2 = 12.496913579752 Factor a perfect square on the left side: (x + 0.05555555555)(x + 0.05555555555) = 12.496913579752 Calculate the square root of the right side: 3.535097393 Break this problem into two subproblems by setting (x + 0.05555555555) equal to 3.535097393 and -3.535097393.Subproblem 1
x + 0.05555555555 = 3.535097393 Simplifying x + 0.05555555555 = 3.535097393 Reorder the terms: 0.05555555555 + x = 3.535097393 Solving 0.05555555555 + x = 3.535097393 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 = 3.535097393 + -0.05555555555 Combine like terms: 0.05555555555 + -0.05555555555 = 0.00000000000 0.00000000000 + x = 3.535097393 + -0.05555555555 x = 3.535097393 + -0.05555555555 Combine like terms: 3.535097393 + -0.05555555555 = 3.47954183745 x = 3.47954183745 Simplifying x = 3.47954183745Subproblem 2
x + 0.05555555555 = -3.535097393 Simplifying x + 0.05555555555 = -3.535097393 Reorder the terms: 0.05555555555 + x = -3.535097393 Solving 0.05555555555 + x = -3.535097393 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 = -3.535097393 + -0.05555555555 Combine like terms: 0.05555555555 + -0.05555555555 = 0.00000000000 0.00000000000 + x = -3.535097393 + -0.05555555555 x = -3.535097393 + -0.05555555555 Combine like terms: -3.535097393 + -0.05555555555 = -3.59065294855 x = -3.59065294855 Simplifying x = -3.59065294855Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.47954183745, -3.59065294855}
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