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Simplifying 0.3333333x2 + 7x + -7 = -1x + 1 Reorder the terms: -7 + 7x + 0.3333333x2 = -1x + 1 Reorder the terms: -7 + 7x + 0.3333333x2 = 1 + -1x Solving -7 + 7x + 0.3333333x2 = 1 + -1x Solving for variable 'x'. Reorder the terms: -7 + -1 + 7x + x + 0.3333333x2 = 1 + -1x + -1 + x Combine like terms: -7 + -1 = -8 -8 + 7x + x + 0.3333333x2 = 1 + -1x + -1 + x Combine like terms: 7x + x = 8x -8 + 8x + 0.3333333x2 = 1 + -1x + -1 + x Reorder the terms: -8 + 8x + 0.3333333x2 = 1 + -1 + -1x + x Combine like terms: 1 + -1 = 0 -8 + 8x + 0.3333333x2 = 0 + -1x + x -8 + 8x + 0.3333333x2 = -1x + x Combine like terms: -1x + x = 0 -8 + 8x + 0.3333333x2 = 0 Begin completing the square. Divide all terms by 0.3333333 the coefficient of the squared term: Divide each side by '0.3333333'. -24.0000024 + 24.0000024x + x2 = 0 Move the constant term to the right: Add '24.0000024' to each side of the equation. -24.0000024 + 24.0000024x + 24.0000024 + x2 = 0 + 24.0000024 Reorder the terms: -24.0000024 + 24.0000024 + 24.0000024x + x2 = 0 + 24.0000024 Combine like terms: -24.0000024 + 24.0000024 = 0.0000000 0.0000000 + 24.0000024x + x2 = 0 + 24.0000024 24.0000024x + x2 = 0 + 24.0000024 Combine like terms: 0 + 24.0000024 = 24.0000024 24.0000024x + x2 = 24.0000024 The x term is 24.0000024x. Take half its coefficient (12.0000012). Square it (144.0000288) and add it to both sides. Add '144.0000288' to each side of the equation. 24.0000024x + 144.0000288 + x2 = 24.0000024 + 144.0000288 Reorder the terms: 144.0000288 + 24.0000024x + x2 = 24.0000024 + 144.0000288 Combine like terms: 24.0000024 + 144.0000288 = 168.0000312 144.0000288 + 24.0000024x + x2 = 168.0000312 Factor a perfect square on the left side: (x + 12.0000012)(x + 12.0000012) = 168.0000312 Calculate the square root of the right side: 12.9614826 Break this problem into two subproblems by setting (x + 12.0000012) equal to 12.9614826 and -12.9614826.Subproblem 1
x + 12.0000012 = 12.9614826 Simplifying x + 12.0000012 = 12.9614826 Reorder the terms: 12.0000012 + x = 12.9614826 Solving 12.0000012 + x = 12.9614826 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.0000012' to each side of the equation. 12.0000012 + -12.0000012 + x = 12.9614826 + -12.0000012 Combine like terms: 12.0000012 + -12.0000012 = 0.0000000 0.0000000 + x = 12.9614826 + -12.0000012 x = 12.9614826 + -12.0000012 Combine like terms: 12.9614826 + -12.0000012 = 0.9614814 x = 0.9614814 Simplifying x = 0.9614814Subproblem 2
x + 12.0000012 = -12.9614826 Simplifying x + 12.0000012 = -12.9614826 Reorder the terms: 12.0000012 + x = -12.9614826 Solving 12.0000012 + x = -12.9614826 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.0000012' to each side of the equation. 12.0000012 + -12.0000012 + x = -12.9614826 + -12.0000012 Combine like terms: 12.0000012 + -12.0000012 = 0.0000000 0.0000000 + x = -12.9614826 + -12.0000012 x = -12.9614826 + -12.0000012 Combine like terms: -12.9614826 + -12.0000012 = -24.9614838 x = -24.9614838 Simplifying x = -24.9614838Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9614814, -24.9614838}
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