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Simplifying 13x2 + -11x + 2 = 0 Reorder the terms: 2 + -11x + 13x2 = 0 Solving 2 + -11x + 13x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. 0.1538461538 + -0.8461538462x + x2 = 0 Move the constant term to the right: Add '-0.1538461538' to each side of the equation. 0.1538461538 + -0.8461538462x + -0.1538461538 + x2 = 0 + -0.1538461538 Reorder the terms: 0.1538461538 + -0.1538461538 + -0.8461538462x + x2 = 0 + -0.1538461538 Combine like terms: 0.1538461538 + -0.1538461538 = 0.0000000000 0.0000000000 + -0.8461538462x + x2 = 0 + -0.1538461538 -0.8461538462x + x2 = 0 + -0.1538461538 Combine like terms: 0 + -0.1538461538 = -0.1538461538 -0.8461538462x + x2 = -0.1538461538 The x term is -0.8461538462x. Take half its coefficient (-0.4230769231). Square it (0.1789940829) and add it to both sides. Add '0.1789940829' to each side of the equation. -0.8461538462x + 0.1789940829 + x2 = -0.1538461538 + 0.1789940829 Reorder the terms: 0.1789940829 + -0.8461538462x + x2 = -0.1538461538 + 0.1789940829 Combine like terms: -0.1538461538 + 0.1789940829 = 0.0251479291 0.1789940829 + -0.8461538462x + x2 = 0.0251479291 Factor a perfect square on the left side: (x + -0.4230769231)(x + -0.4230769231) = 0.0251479291 Calculate the square root of the right side: 0.158580986 Break this problem into two subproblems by setting (x + -0.4230769231) equal to 0.158580986 and -0.158580986.Subproblem 1
x + -0.4230769231 = 0.158580986 Simplifying x + -0.4230769231 = 0.158580986 Reorder the terms: -0.4230769231 + x = 0.158580986 Solving -0.4230769231 + x = 0.158580986 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4230769231' to each side of the equation. -0.4230769231 + 0.4230769231 + x = 0.158580986 + 0.4230769231 Combine like terms: -0.4230769231 + 0.4230769231 = 0.0000000000 0.0000000000 + x = 0.158580986 + 0.4230769231 x = 0.158580986 + 0.4230769231 Combine like terms: 0.158580986 + 0.4230769231 = 0.5816579091 x = 0.5816579091 Simplifying x = 0.5816579091Subproblem 2
x + -0.4230769231 = -0.158580986 Simplifying x + -0.4230769231 = -0.158580986 Reorder the terms: -0.4230769231 + x = -0.158580986 Solving -0.4230769231 + x = -0.158580986 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4230769231' to each side of the equation. -0.4230769231 + 0.4230769231 + x = -0.158580986 + 0.4230769231 Combine like terms: -0.4230769231 + 0.4230769231 = 0.0000000000 0.0000000000 + x = -0.158580986 + 0.4230769231 x = -0.158580986 + 0.4230769231 Combine like terms: -0.158580986 + 0.4230769231 = 0.2644959371 x = 0.2644959371 Simplifying x = 0.2644959371Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5816579091, 0.2644959371}
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