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Simplifying 54x2 + -263x = -184 Reorder the terms: -263x + 54x2 = -184 Solving -263x + 54x2 = -184 Solving for variable 'x'. Reorder the terms: 184 + -263x + 54x2 = -184 + 184 Combine like terms: -184 + 184 = 0 184 + -263x + 54x2 = 0 Begin completing the square. Divide all terms by 54 the coefficient of the squared term: Divide each side by '54'. 3.407407407 + -4.87037037x + x2 = 0 Move the constant term to the right: Add '-3.407407407' to each side of the equation. 3.407407407 + -4.87037037x + -3.407407407 + x2 = 0 + -3.407407407 Reorder the terms: 3.407407407 + -3.407407407 + -4.87037037x + x2 = 0 + -3.407407407 Combine like terms: 3.407407407 + -3.407407407 = 0.000000000 0.000000000 + -4.87037037x + x2 = 0 + -3.407407407 -4.87037037x + x2 = 0 + -3.407407407 Combine like terms: 0 + -3.407407407 = -3.407407407 -4.87037037x + x2 = -3.407407407 The x term is -4.87037037x. Take half its coefficient (-2.435185185). Square it (5.930126885) and add it to both sides. Add '5.930126885' to each side of the equation. -4.87037037x + 5.930126885 + x2 = -3.407407407 + 5.930126885 Reorder the terms: 5.930126885 + -4.87037037x + x2 = -3.407407407 + 5.930126885 Combine like terms: -3.407407407 + 5.930126885 = 2.522719478 5.930126885 + -4.87037037x + x2 = 2.522719478 Factor a perfect square on the left side: (x + -2.435185185)(x + -2.435185185) = 2.522719478 Calculate the square root of the right side: 1.588307111 Break this problem into two subproblems by setting (x + -2.435185185) equal to 1.588307111 and -1.588307111.Subproblem 1
x + -2.435185185 = 1.588307111 Simplifying x + -2.435185185 = 1.588307111 Reorder the terms: -2.435185185 + x = 1.588307111 Solving -2.435185185 + x = 1.588307111 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.435185185' to each side of the equation. -2.435185185 + 2.435185185 + x = 1.588307111 + 2.435185185 Combine like terms: -2.435185185 + 2.435185185 = 0.000000000 0.000000000 + x = 1.588307111 + 2.435185185 x = 1.588307111 + 2.435185185 Combine like terms: 1.588307111 + 2.435185185 = 4.023492296 x = 4.023492296 Simplifying x = 4.023492296Subproblem 2
x + -2.435185185 = -1.588307111 Simplifying x + -2.435185185 = -1.588307111 Reorder the terms: -2.435185185 + x = -1.588307111 Solving -2.435185185 + x = -1.588307111 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.435185185' to each side of the equation. -2.435185185 + 2.435185185 + x = -1.588307111 + 2.435185185 Combine like terms: -2.435185185 + 2.435185185 = 0.000000000 0.000000000 + x = -1.588307111 + 2.435185185 x = -1.588307111 + 2.435185185 Combine like terms: -1.588307111 + 2.435185185 = 0.846878074 x = 0.846878074 Simplifying x = 0.846878074Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.023492296, 0.846878074}
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