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Simplifying 529 = 54x2 + -263x + 834 Reorder the terms: 529 = 834 + -263x + 54x2 Solving 529 = 834 + -263x + 54x2 Solving for variable 'x'. Combine like terms: 529 + -834 = -305 -305 + 263x + -54x2 = 834 + -263x + 54x2 + -834 + 263x + -54x2 Reorder the terms: -305 + 263x + -54x2 = 834 + -834 + -263x + 263x + 54x2 + -54x2 Combine like terms: 834 + -834 = 0 -305 + 263x + -54x2 = 0 + -263x + 263x + 54x2 + -54x2 -305 + 263x + -54x2 = -263x + 263x + 54x2 + -54x2 Combine like terms: -263x + 263x = 0 -305 + 263x + -54x2 = 0 + 54x2 + -54x2 -305 + 263x + -54x2 = 54x2 + -54x2 Combine like terms: 54x2 + -54x2 = 0 -305 + 263x + -54x2 = 0 Begin completing the square. Divide all terms by -54 the coefficient of the squared term: Divide each side by '-54'. 5.648148148 + -4.87037037x + x2 = 0 Move the constant term to the right: Add '-5.648148148' to each side of the equation. 5.648148148 + -4.87037037x + -5.648148148 + x2 = 0 + -5.648148148 Reorder the terms: 5.648148148 + -5.648148148 + -4.87037037x + x2 = 0 + -5.648148148 Combine like terms: 5.648148148 + -5.648148148 = 0.000000000 0.000000000 + -4.87037037x + x2 = 0 + -5.648148148 -4.87037037x + x2 = 0 + -5.648148148 Combine like terms: 0 + -5.648148148 = -5.648148148 -4.87037037x + x2 = -5.648148148 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 = -5.648148148 + 5.930126885 Reorder the terms: 5.930126885 + -4.87037037x + x2 = -5.648148148 + 5.930126885 Combine like terms: -5.648148148 + 5.930126885 = 0.281978737 5.930126885 + -4.87037037x + x2 = 0.281978737 Factor a perfect square on the left side: (x + -2.435185185)(x + -2.435185185) = 0.281978737 Calculate the square root of the right side: 0.531016701 Break this problem into two subproblems by setting (x + -2.435185185) equal to 0.531016701 and -0.531016701.Subproblem 1
x + -2.435185185 = 0.531016701 Simplifying x + -2.435185185 = 0.531016701 Reorder the terms: -2.435185185 + x = 0.531016701 Solving -2.435185185 + x = 0.531016701 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 = 0.531016701 + 2.435185185 Combine like terms: -2.435185185 + 2.435185185 = 0.000000000 0.000000000 + x = 0.531016701 + 2.435185185 x = 0.531016701 + 2.435185185 Combine like terms: 0.531016701 + 2.435185185 = 2.966201886 x = 2.966201886 Simplifying x = 2.966201886Subproblem 2
x + -2.435185185 = -0.531016701 Simplifying x + -2.435185185 = -0.531016701 Reorder the terms: -2.435185185 + x = -0.531016701 Solving -2.435185185 + x = -0.531016701 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 = -0.531016701 + 2.435185185 Combine like terms: -2.435185185 + 2.435185185 = 0.000000000 0.000000000 + x = -0.531016701 + 2.435185185 x = -0.531016701 + 2.435185185 Combine like terms: -0.531016701 + 2.435185185 = 1.904168484 x = 1.904168484 Simplifying x = 1.904168484Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.966201886, 1.904168484}
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