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Simplifying 13x2 + -11x + 1 = 0 Reorder the terms: 1 + -11x + 13x2 = 0 Solving 1 + -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'. 0.07692307692 + -0.8461538462x + x2 = 0 Move the constant term to the right: Add '-0.07692307692' to each side of the equation. 0.07692307692 + -0.8461538462x + -0.07692307692 + x2 = 0 + -0.07692307692 Reorder the terms: 0.07692307692 + -0.07692307692 + -0.8461538462x + x2 = 0 + -0.07692307692 Combine like terms: 0.07692307692 + -0.07692307692 = 0.00000000000 0.00000000000 + -0.8461538462x + x2 = 0 + -0.07692307692 -0.8461538462x + x2 = 0 + -0.07692307692 Combine like terms: 0 + -0.07692307692 = -0.07692307692 -0.8461538462x + x2 = -0.07692307692 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 = -0.07692307692 + 0.1789940829 Reorder the terms: 0.1789940829 + -0.8461538462x + x2 = -0.07692307692 + 0.1789940829 Combine like terms: -0.07692307692 + 0.1789940829 = 0.10207100598 0.1789940829 + -0.8461538462x + x2 = 0.10207100598 Factor a perfect square on the left side: (x + -0.4230769231)(x + -0.4230769231) = 0.10207100598 Calculate the square root of the right side: 0.319485533 Break this problem into two subproblems by setting (x + -0.4230769231) equal to 0.319485533 and -0.319485533.Subproblem 1
x + -0.4230769231 = 0.319485533 Simplifying x + -0.4230769231 = 0.319485533 Reorder the terms: -0.4230769231 + x = 0.319485533 Solving -0.4230769231 + x = 0.319485533 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 = 0.319485533 + 0.4230769231 Combine like terms: -0.4230769231 + 0.4230769231 = 0.0000000000 0.0000000000 + x = 0.319485533 + 0.4230769231 x = 0.319485533 + 0.4230769231 Combine like terms: 0.319485533 + 0.4230769231 = 0.7425624561 x = 0.7425624561 Simplifying x = 0.7425624561Subproblem 2
x + -0.4230769231 = -0.319485533 Simplifying x + -0.4230769231 = -0.319485533 Reorder the terms: -0.4230769231 + x = -0.319485533 Solving -0.4230769231 + x = -0.319485533 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 = -0.319485533 + 0.4230769231 Combine like terms: -0.4230769231 + 0.4230769231 = 0.0000000000 0.0000000000 + x = -0.319485533 + 0.4230769231 x = -0.319485533 + 0.4230769231 Combine like terms: -0.319485533 + 0.4230769231 = 0.1035913901 x = 0.1035913901 Simplifying x = 0.1035913901Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7425624561, 0.1035913901}
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