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Simplifying 655 = 54x2 + -263x + 833 Reorder the terms: 655 = 833 + -263x + 54x2 Solving 655 = 833 + -263x + 54x2 Solving for variable 'x'. Combine like terms: 655 + -833 = -178 -178 + 263x + -54x2 = 833 + -263x + 54x2 + -833 + 263x + -54x2 Reorder the terms: -178 + 263x + -54x2 = 833 + -833 + -263x + 263x + 54x2 + -54x2 Combine like terms: 833 + -833 = 0 -178 + 263x + -54x2 = 0 + -263x + 263x + 54x2 + -54x2 -178 + 263x + -54x2 = -263x + 263x + 54x2 + -54x2 Combine like terms: -263x + 263x = 0 -178 + 263x + -54x2 = 0 + 54x2 + -54x2 -178 + 263x + -54x2 = 54x2 + -54x2 Combine like terms: 54x2 + -54x2 = 0 -178 + 263x + -54x2 = 0 Begin completing the square. Divide all terms by -54 the coefficient of the squared term: Divide each side by '-54'. 3.296296296 + -4.87037037x + x2 = 0 Move the constant term to the right: Add '-3.296296296' to each side of the equation. 3.296296296 + -4.87037037x + -3.296296296 + x2 = 0 + -3.296296296 Reorder the terms: 3.296296296 + -3.296296296 + -4.87037037x + x2 = 0 + -3.296296296 Combine like terms: 3.296296296 + -3.296296296 = 0.000000000 0.000000000 + -4.87037037x + x2 = 0 + -3.296296296 -4.87037037x + x2 = 0 + -3.296296296 Combine like terms: 0 + -3.296296296 = -3.296296296 -4.87037037x + x2 = -3.296296296 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 = -3.296296296 + 5.930126885 Reorder the terms: 5.930126885 + -4.87037037x + x2 = -3.296296296 + 5.930126885 Combine like terms: -3.296296296 + 5.930126885 = 2.633830589 5.930126885 + -4.87037037x + x2 = 2.633830589 Factor a perfect square on the left side: (x + -2.435185185)(x + -2.435185185) = 2.633830589 Calculate the square root of the right side: 1.622908065 Break this problem into two subproblems by setting (x + -2.435185185) equal to 1.622908065 and -1.622908065.Subproblem 1
x + -2.435185185 = 1.622908065 Simplifying x + -2.435185185 = 1.622908065 Reorder the terms: -2.435185185 + x = 1.622908065 Solving -2.435185185 + x = 1.622908065 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 = 1.622908065 + 2.435185185 Combine like terms: -2.435185185 + 2.435185185 = 0.000000000 0.000000000 + x = 1.622908065 + 2.435185185 x = 1.622908065 + 2.435185185 Combine like terms: 1.622908065 + 2.435185185 = 4.05809325 x = 4.05809325 Simplifying x = 4.05809325Subproblem 2
x + -2.435185185 = -1.622908065 Simplifying x + -2.435185185 = -1.622908065 Reorder the terms: -2.435185185 + x = -1.622908065 Solving -2.435185185 + x = -1.622908065 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 = -1.622908065 + 2.435185185 Combine like terms: -2.435185185 + 2.435185185 = 0.000000000 0.000000000 + x = -1.622908065 + 2.435185185 x = -1.622908065 + 2.435185185 Combine like terms: -1.622908065 + 2.435185185 = 0.81227712 x = 0.81227712 Simplifying x = 0.81227712Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.05809325, 0.81227712}
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