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Simplifying 36x2 + 4x + -33 = 0 Reorder the terms: -33 + 4x + 36x2 = 0 Solving -33 + 4x + 36x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. -0.9166666667 + 0.1111111111x + x2 = 0 Move the constant term to the right: Add '0.9166666667' to each side of the equation. -0.9166666667 + 0.1111111111x + 0.9166666667 + x2 = 0 + 0.9166666667 Reorder the terms: -0.9166666667 + 0.9166666667 + 0.1111111111x + x2 = 0 + 0.9166666667 Combine like terms: -0.9166666667 + 0.9166666667 = 0.0000000000 0.0000000000 + 0.1111111111x + x2 = 0 + 0.9166666667 0.1111111111x + x2 = 0 + 0.9166666667 Combine like terms: 0 + 0.9166666667 = 0.9166666667 0.1111111111x + x2 = 0.9166666667 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 = 0.9166666667 + 0.003086419752 Reorder the terms: 0.003086419752 + 0.1111111111x + x2 = 0.9166666667 + 0.003086419752 Combine like terms: 0.9166666667 + 0.003086419752 = 0.919753086452 0.003086419752 + 0.1111111111x + x2 = 0.919753086452 Factor a perfect square on the left side: (x + 0.05555555555)(x + 0.05555555555) = 0.919753086452 Calculate the square root of the right side: 0.959037583 Break this problem into two subproblems by setting (x + 0.05555555555) equal to 0.959037583 and -0.959037583.Subproblem 1
x + 0.05555555555 = 0.959037583 Simplifying x + 0.05555555555 = 0.959037583 Reorder the terms: 0.05555555555 + x = 0.959037583 Solving 0.05555555555 + x = 0.959037583 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 = 0.959037583 + -0.05555555555 Combine like terms: 0.05555555555 + -0.05555555555 = 0.00000000000 0.00000000000 + x = 0.959037583 + -0.05555555555 x = 0.959037583 + -0.05555555555 Combine like terms: 0.959037583 + -0.05555555555 = 0.90348202745 x = 0.90348202745 Simplifying x = 0.90348202745Subproblem 2
x + 0.05555555555 = -0.959037583 Simplifying x + 0.05555555555 = -0.959037583 Reorder the terms: 0.05555555555 + x = -0.959037583 Solving 0.05555555555 + x = -0.959037583 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 = -0.959037583 + -0.05555555555 Combine like terms: 0.05555555555 + -0.05555555555 = 0.00000000000 0.00000000000 + x = -0.959037583 + -0.05555555555 x = -0.959037583 + -0.05555555555 Combine like terms: -0.959037583 + -0.05555555555 = -1.01459313855 x = -1.01459313855 Simplifying x = -1.01459313855Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.90348202745, -1.01459313855}
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