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Simplifying 43x + -7x2 = 766x + -23 Reorder the terms: 43x + -7x2 = -23 + 766x Solving 43x + -7x2 = -23 + 766x Solving for variable 'x'. Reorder the terms: 23 + 43x + -766x + -7x2 = -23 + 766x + 23 + -766x Combine like terms: 43x + -766x = -723x 23 + -723x + -7x2 = -23 + 766x + 23 + -766x Reorder the terms: 23 + -723x + -7x2 = -23 + 23 + 766x + -766x Combine like terms: -23 + 23 = 0 23 + -723x + -7x2 = 0 + 766x + -766x 23 + -723x + -7x2 = 766x + -766x Combine like terms: 766x + -766x = 0 23 + -723x + -7x2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -3.285714286 + 103.2857143x + x2 = 0 Move the constant term to the right: Add '3.285714286' to each side of the equation. -3.285714286 + 103.2857143x + 3.285714286 + x2 = 0 + 3.285714286 Reorder the terms: -3.285714286 + 3.285714286 + 103.2857143x + x2 = 0 + 3.285714286 Combine like terms: -3.285714286 + 3.285714286 = 0.000000000 0.000000000 + 103.2857143x + x2 = 0 + 3.285714286 103.2857143x + x2 = 0 + 3.285714286 Combine like terms: 0 + 3.285714286 = 3.285714286 103.2857143x + x2 = 3.285714286 The x term is 103.2857143x. Take half its coefficient (51.64285715). Square it (2666.984695) and add it to both sides. Add '2666.984695' to each side of the equation. 103.2857143x + 2666.984695 + x2 = 3.285714286 + 2666.984695 Reorder the terms: 2666.984695 + 103.2857143x + x2 = 3.285714286 + 2666.984695 Combine like terms: 3.285714286 + 2666.984695 = 2670.270409286 2666.984695 + 103.2857143x + x2 = 2670.270409286 Factor a perfect square on the left side: (x + 51.64285715)(x + 51.64285715) = 2670.270409286 Calculate the square root of the right side: 51.674659257 Break this problem into two subproblems by setting (x + 51.64285715) equal to 51.674659257 and -51.674659257.Subproblem 1
x + 51.64285715 = 51.674659257 Simplifying x + 51.64285715 = 51.674659257 Reorder the terms: 51.64285715 + x = 51.674659257 Solving 51.64285715 + x = 51.674659257 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-51.64285715' to each side of the equation. 51.64285715 + -51.64285715 + x = 51.674659257 + -51.64285715 Combine like terms: 51.64285715 + -51.64285715 = 0.00000000 0.00000000 + x = 51.674659257 + -51.64285715 x = 51.674659257 + -51.64285715 Combine like terms: 51.674659257 + -51.64285715 = 0.031802107 x = 0.031802107 Simplifying x = 0.031802107Subproblem 2
x + 51.64285715 = -51.674659257 Simplifying x + 51.64285715 = -51.674659257 Reorder the terms: 51.64285715 + x = -51.674659257 Solving 51.64285715 + x = -51.674659257 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-51.64285715' to each side of the equation. 51.64285715 + -51.64285715 + x = -51.674659257 + -51.64285715 Combine like terms: 51.64285715 + -51.64285715 = 0.00000000 0.00000000 + x = -51.674659257 + -51.64285715 x = -51.674659257 + -51.64285715 Combine like terms: -51.674659257 + -51.64285715 = -103.317516407 x = -103.317516407 Simplifying x = -103.317516407Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.031802107, -103.317516407}
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