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Simplifying 31x2 + -26x + -8 = 0 Reorder the terms: -8 + -26x + 31x2 = 0 Solving -8 + -26x + 31x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 31 the coefficient of the squared term: Divide each side by '31'. -0.2580645161 + -0.8387096774x + x2 = 0 Move the constant term to the right: Add '0.2580645161' to each side of the equation. -0.2580645161 + -0.8387096774x + 0.2580645161 + x2 = 0 + 0.2580645161 Reorder the terms: -0.2580645161 + 0.2580645161 + -0.8387096774x + x2 = 0 + 0.2580645161 Combine like terms: -0.2580645161 + 0.2580645161 = 0.0000000000 0.0000000000 + -0.8387096774x + x2 = 0 + 0.2580645161 -0.8387096774x + x2 = 0 + 0.2580645161 Combine like terms: 0 + 0.2580645161 = 0.2580645161 -0.8387096774x + x2 = 0.2580645161 The x term is -0.8387096774x. Take half its coefficient (-0.4193548387). Square it (0.1758584807) and add it to both sides. Add '0.1758584807' to each side of the equation. -0.8387096774x + 0.1758584807 + x2 = 0.2580645161 + 0.1758584807 Reorder the terms: 0.1758584807 + -0.8387096774x + x2 = 0.2580645161 + 0.1758584807 Combine like terms: 0.2580645161 + 0.1758584807 = 0.4339229968 0.1758584807 + -0.8387096774x + x2 = 0.4339229968 Factor a perfect square on the left side: (x + -0.4193548387)(x + -0.4193548387) = 0.4339229968 Calculate the square root of the right side: 0.658728318 Break this problem into two subproblems by setting (x + -0.4193548387) equal to 0.658728318 and -0.658728318.Subproblem 1
x + -0.4193548387 = 0.658728318 Simplifying x + -0.4193548387 = 0.658728318 Reorder the terms: -0.4193548387 + x = 0.658728318 Solving -0.4193548387 + x = 0.658728318 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4193548387' to each side of the equation. -0.4193548387 + 0.4193548387 + x = 0.658728318 + 0.4193548387 Combine like terms: -0.4193548387 + 0.4193548387 = 0.0000000000 0.0000000000 + x = 0.658728318 + 0.4193548387 x = 0.658728318 + 0.4193548387 Combine like terms: 0.658728318 + 0.4193548387 = 1.0780831567 x = 1.0780831567 Simplifying x = 1.0780831567Subproblem 2
x + -0.4193548387 = -0.658728318 Simplifying x + -0.4193548387 = -0.658728318 Reorder the terms: -0.4193548387 + x = -0.658728318 Solving -0.4193548387 + x = -0.658728318 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4193548387' to each side of the equation. -0.4193548387 + 0.4193548387 + x = -0.658728318 + 0.4193548387 Combine like terms: -0.4193548387 + 0.4193548387 = 0.0000000000 0.0000000000 + x = -0.658728318 + 0.4193548387 x = -0.658728318 + 0.4193548387 Combine like terms: -0.658728318 + 0.4193548387 = -0.2393734793 x = -0.2393734793 Simplifying x = -0.2393734793Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0780831567, -0.2393734793}
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