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Simplifying 2 + -1x + -0.33333x2 = 0 Solving 2 + -1x + -0.33333x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.33333 the coefficient of the squared term: Divide each side by '-0.33333'. -6.000060001 + 3.00003x + x2 = 0 Move the constant term to the right: Add '6.000060001' to each side of the equation. -6.000060001 + 3.00003x + 6.000060001 + x2 = 0 + 6.000060001 Reorder the terms: -6.000060001 + 6.000060001 + 3.00003x + x2 = 0 + 6.000060001 Combine like terms: -6.000060001 + 6.000060001 = 0.000000000 0.000000000 + 3.00003x + x2 = 0 + 6.000060001 3.00003x + x2 = 0 + 6.000060001 Combine like terms: 0 + 6.000060001 = 6.000060001 3.00003x + x2 = 6.000060001 The x term is 3.00003x. Take half its coefficient (1.500015). Square it (2.250045000) and add it to both sides. Add '2.250045000' to each side of the equation. 3.00003x + 2.250045000 + x2 = 6.000060001 + 2.250045000 Reorder the terms: 2.250045000 + 3.00003x + x2 = 6.000060001 + 2.250045000 Combine like terms: 6.000060001 + 2.250045000 = 8.250105001 2.250045000 + 3.00003x + x2 = 8.250105001 Factor a perfect square on the left side: (x + 1.500015)(x + 1.500015) = 8.250105001 Calculate the square root of the right side: 2.872299602 Break this problem into two subproblems by setting (x + 1.500015) equal to 2.872299602 and -2.872299602.Subproblem 1
x + 1.500015 = 2.872299602 Simplifying x + 1.500015 = 2.872299602 Reorder the terms: 1.500015 + x = 2.872299602 Solving 1.500015 + x = 2.872299602 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.500015' to each side of the equation. 1.500015 + -1.500015 + x = 2.872299602 + -1.500015 Combine like terms: 1.500015 + -1.500015 = 0.000000 0.000000 + x = 2.872299602 + -1.500015 x = 2.872299602 + -1.500015 Combine like terms: 2.872299602 + -1.500015 = 1.372284602 x = 1.372284602 Simplifying x = 1.372284602Subproblem 2
x + 1.500015 = -2.872299602 Simplifying x + 1.500015 = -2.872299602 Reorder the terms: 1.500015 + x = -2.872299602 Solving 1.500015 + x = -2.872299602 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.500015' to each side of the equation. 1.500015 + -1.500015 + x = -2.872299602 + -1.500015 Combine like terms: 1.500015 + -1.500015 = 0.000000 0.000000 + x = -2.872299602 + -1.500015 x = -2.872299602 + -1.500015 Combine like terms: -2.872299602 + -1.500015 = -4.372314602 x = -4.372314602 Simplifying x = -4.372314602Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.372284602, -4.372314602}
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