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Simplifying 810 = 54x2 + -263x + 834 Reorder the terms: 810 = 834 + -263x + 54x2 Solving 810 = 834 + -263x + 54x2 Solving for variable 'x'. Combine like terms: 810 + -834 = -24 -24 + 263x + -54x2 = 834 + -263x + 54x2 + -834 + 263x + -54x2 Reorder the terms: -24 + 263x + -54x2 = 834 + -834 + -263x + 263x + 54x2 + -54x2 Combine like terms: 834 + -834 = 0 -24 + 263x + -54x2 = 0 + -263x + 263x + 54x2 + -54x2 -24 + 263x + -54x2 = -263x + 263x + 54x2 + -54x2 Combine like terms: -263x + 263x = 0 -24 + 263x + -54x2 = 0 + 54x2 + -54x2 -24 + 263x + -54x2 = 54x2 + -54x2 Combine like terms: 54x2 + -54x2 = 0 -24 + 263x + -54x2 = 0 Begin completing the square. Divide all terms by -54 the coefficient of the squared term: Divide each side by '-54'. 0.4444444444 + -4.87037037x + x2 = 0 Move the constant term to the right: Add '-0.4444444444' to each side of the equation. 0.4444444444 + -4.87037037x + -0.4444444444 + x2 = 0 + -0.4444444444 Reorder the terms: 0.4444444444 + -0.4444444444 + -4.87037037x + x2 = 0 + -0.4444444444 Combine like terms: 0.4444444444 + -0.4444444444 = 0.0000000000 0.0000000000 + -4.87037037x + x2 = 0 + -0.4444444444 -4.87037037x + x2 = 0 + -0.4444444444 Combine like terms: 0 + -0.4444444444 = -0.4444444444 -4.87037037x + x2 = -0.4444444444 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 = -0.4444444444 + 5.930126885 Reorder the terms: 5.930126885 + -4.87037037x + x2 = -0.4444444444 + 5.930126885 Combine like terms: -0.4444444444 + 5.930126885 = 5.4856824406 5.930126885 + -4.87037037x + x2 = 5.4856824406 Factor a perfect square on the left side: (x + -2.435185185)(x + -2.435185185) = 5.4856824406 Calculate the square root of the right side: 2.342153377 Break this problem into two subproblems by setting (x + -2.435185185) equal to 2.342153377 and -2.342153377.Subproblem 1
x + -2.435185185 = 2.342153377 Simplifying x + -2.435185185 = 2.342153377 Reorder the terms: -2.435185185 + x = 2.342153377 Solving -2.435185185 + x = 2.342153377 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 = 2.342153377 + 2.435185185 Combine like terms: -2.435185185 + 2.435185185 = 0.000000000 0.000000000 + x = 2.342153377 + 2.435185185 x = 2.342153377 + 2.435185185 Combine like terms: 2.342153377 + 2.435185185 = 4.777338562 x = 4.777338562 Simplifying x = 4.777338562Subproblem 2
x + -2.435185185 = -2.342153377 Simplifying x + -2.435185185 = -2.342153377 Reorder the terms: -2.435185185 + x = -2.342153377 Solving -2.435185185 + x = -2.342153377 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 = -2.342153377 + 2.435185185 Combine like terms: -2.435185185 + 2.435185185 = 0.000000000 0.000000000 + x = -2.342153377 + 2.435185185 x = -2.342153377 + 2.435185185 Combine like terms: -2.342153377 + 2.435185185 = 0.093031808 x = 0.093031808 Simplifying x = 0.093031808Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.777338562, 0.093031808}
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