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Simplifying 36x2 + -121x + 16 = 0 Reorder the terms: 16 + -121x + 36x2 = 0 Solving 16 + -121x + 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'. 0.4444444444 + -3.361111111x + x2 = 0 Move the constant term to the right: Add '-0.4444444444' to each side of the equation. 0.4444444444 + -3.361111111x + -0.4444444444 + x2 = 0 + -0.4444444444 Reorder the terms: 0.4444444444 + -0.4444444444 + -3.361111111x + x2 = 0 + -0.4444444444 Combine like terms: 0.4444444444 + -0.4444444444 = 0.0000000000 0.0000000000 + -3.361111111x + x2 = 0 + -0.4444444444 -3.361111111x + x2 = 0 + -0.4444444444 Combine like terms: 0 + -0.4444444444 = -0.4444444444 -3.361111111x + x2 = -0.4444444444 The x term is -3.361111111x. Take half its coefficient (-1.680555556). Square it (2.824266977) and add it to both sides. Add '2.824266977' to each side of the equation. -3.361111111x + 2.824266977 + x2 = -0.4444444444 + 2.824266977 Reorder the terms: 2.824266977 + -3.361111111x + x2 = -0.4444444444 + 2.824266977 Combine like terms: -0.4444444444 + 2.824266977 = 2.3798225326 2.824266977 + -3.361111111x + x2 = 2.3798225326 Factor a perfect square on the left side: (x + -1.680555556)(x + -1.680555556) = 2.3798225326 Calculate the square root of the right side: 1.542667343 Break this problem into two subproblems by setting (x + -1.680555556) equal to 1.542667343 and -1.542667343.Subproblem 1
x + -1.680555556 = 1.542667343 Simplifying x + -1.680555556 = 1.542667343 Reorder the terms: -1.680555556 + x = 1.542667343 Solving -1.680555556 + x = 1.542667343 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.680555556' to each side of the equation. -1.680555556 + 1.680555556 + x = 1.542667343 + 1.680555556 Combine like terms: -1.680555556 + 1.680555556 = 0.000000000 0.000000000 + x = 1.542667343 + 1.680555556 x = 1.542667343 + 1.680555556 Combine like terms: 1.542667343 + 1.680555556 = 3.223222899 x = 3.223222899 Simplifying x = 3.223222899Subproblem 2
x + -1.680555556 = -1.542667343 Simplifying x + -1.680555556 = -1.542667343 Reorder the terms: -1.680555556 + x = -1.542667343 Solving -1.680555556 + x = -1.542667343 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.680555556' to each side of the equation. -1.680555556 + 1.680555556 + x = -1.542667343 + 1.680555556 Combine like terms: -1.680555556 + 1.680555556 = 0.000000000 0.000000000 + x = -1.542667343 + 1.680555556 x = -1.542667343 + 1.680555556 Combine like terms: -1.542667343 + 1.680555556 = 0.137888213 x = 0.137888213 Simplifying x = 0.137888213Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.223222899, 0.137888213}
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