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Simplifying 5x + 2 = -1.8x2 + -6x + 222 Reorder the terms: 2 + 5x = -1.8x2 + -6x + 222 Reorder the terms: 2 + 5x = 222 + -6x + -1.8x2 Solving 2 + 5x = 222 + -6x + -1.8x2 Solving for variable 'x'. Reorder the terms: 2 + -222 + 5x + 6x + 1.8x2 = 222 + -6x + -1.8x2 + -222 + 6x + 1.8x2 Combine like terms: 2 + -222 = -220 -220 + 5x + 6x + 1.8x2 = 222 + -6x + -1.8x2 + -222 + 6x + 1.8x2 Combine like terms: 5x + 6x = 11x -220 + 11x + 1.8x2 = 222 + -6x + -1.8x2 + -222 + 6x + 1.8x2 Reorder the terms: -220 + 11x + 1.8x2 = 222 + -222 + -6x + 6x + -1.8x2 + 1.8x2 Combine like terms: 222 + -222 = 0 -220 + 11x + 1.8x2 = 0 + -6x + 6x + -1.8x2 + 1.8x2 -220 + 11x + 1.8x2 = -6x + 6x + -1.8x2 + 1.8x2 Combine like terms: -6x + 6x = 0 -220 + 11x + 1.8x2 = 0 + -1.8x2 + 1.8x2 -220 + 11x + 1.8x2 = -1.8x2 + 1.8x2 Combine like terms: -1.8x2 + 1.8x2 = 0.0 -220 + 11x + 1.8x2 = 0.0 Begin completing the square. Divide all terms by 1.8 the coefficient of the squared term: Divide each side by '1.8'. -122.2222222 + 6.111111111x + x2 = 0 Move the constant term to the right: Add '122.2222222' to each side of the equation. -122.2222222 + 6.111111111x + 122.2222222 + x2 = 0 + 122.2222222 Reorder the terms: -122.2222222 + 122.2222222 + 6.111111111x + x2 = 0 + 122.2222222 Combine like terms: -122.2222222 + 122.2222222 = 0.0000000 0.0000000 + 6.111111111x + x2 = 0 + 122.2222222 6.111111111x + x2 = 0 + 122.2222222 Combine like terms: 0 + 122.2222222 = 122.2222222 6.111111111x + x2 = 122.2222222 The x term is 6.111111111x. Take half its coefficient (3.055555556). Square it (9.336419756) and add it to both sides. Add '9.336419756' to each side of the equation. 6.111111111x + 9.336419756 + x2 = 122.2222222 + 9.336419756 Reorder the terms: 9.336419756 + 6.111111111x + x2 = 122.2222222 + 9.336419756 Combine like terms: 122.2222222 + 9.336419756 = 131.558641956 9.336419756 + 6.111111111x + x2 = 131.558641956 Factor a perfect square on the left side: (x + 3.055555556)(x + 3.055555556) = 131.558641956 Calculate the square root of the right side: 11.469901567 Break this problem into two subproblems by setting (x + 3.055555556) equal to 11.469901567 and -11.469901567.Subproblem 1
x + 3.055555556 = 11.469901567 Simplifying x + 3.055555556 = 11.469901567 Reorder the terms: 3.055555556 + x = 11.469901567 Solving 3.055555556 + x = 11.469901567 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.055555556' to each side of the equation. 3.055555556 + -3.055555556 + x = 11.469901567 + -3.055555556 Combine like terms: 3.055555556 + -3.055555556 = 0.000000000 0.000000000 + x = 11.469901567 + -3.055555556 x = 11.469901567 + -3.055555556 Combine like terms: 11.469901567 + -3.055555556 = 8.414346011 x = 8.414346011 Simplifying x = 8.414346011Subproblem 2
x + 3.055555556 = -11.469901567 Simplifying x + 3.055555556 = -11.469901567 Reorder the terms: 3.055555556 + x = -11.469901567 Solving 3.055555556 + x = -11.469901567 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.055555556' to each side of the equation. 3.055555556 + -3.055555556 + x = -11.469901567 + -3.055555556 Combine like terms: 3.055555556 + -3.055555556 = 0.000000000 0.000000000 + x = -11.469901567 + -3.055555556 x = -11.469901567 + -3.055555556 Combine like terms: -11.469901567 + -3.055555556 = -14.525457123 x = -14.525457123 Simplifying x = -14.525457123Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.414346011, -14.525457123}
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