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Simplifying x2 = 1.94994 + -6.21x Solving x2 = 1.94994 + -6.21x Solving for variable 'x'. Reorder the terms: -1.94994 + 6.21x + x2 = 1.94994 + -6.21x + -1.94994 + 6.21x Reorder the terms: -1.94994 + 6.21x + x2 = 1.94994 + -1.94994 + -6.21x + 6.21x Combine like terms: 1.94994 + -1.94994 = 0.00000 -1.94994 + 6.21x + x2 = 0.00000 + -6.21x + 6.21x -1.94994 + 6.21x + x2 = -6.21x + 6.21x Combine like terms: -6.21x + 6.21x = 0.00 -1.94994 + 6.21x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '1.94994' to each side of the equation. -1.94994 + 6.21x + 1.94994 + x2 = 0.00 + 1.94994 Reorder the terms: -1.94994 + 1.94994 + 6.21x + x2 = 0.00 + 1.94994 Combine like terms: -1.94994 + 1.94994 = 0.00000 0.00000 + 6.21x + x2 = 0.00 + 1.94994 6.21x + x2 = 0.00 + 1.94994 Combine like terms: 0.00 + 1.94994 = 1.94994 6.21x + x2 = 1.94994 The x term is 6.21x. Take half its coefficient (3.105). Square it (9.641025) and add it to both sides. Add '9.641025' to each side of the equation. 6.21x + 9.641025 + x2 = 1.94994 + 9.641025 Reorder the terms: 9.641025 + 6.21x + x2 = 1.94994 + 9.641025 Combine like terms: 1.94994 + 9.641025 = 11.590965 9.641025 + 6.21x + x2 = 11.590965 Factor a perfect square on the left side: (x + 3.105)(x + 3.105) = 11.590965 Calculate the square root of the right side: 3.404550631 Break this problem into two subproblems by setting (x + 3.105) equal to 3.404550631 and -3.404550631.Subproblem 1
x + 3.105 = 3.404550631 Simplifying x + 3.105 = 3.404550631 Reorder the terms: 3.105 + x = 3.404550631 Solving 3.105 + x = 3.404550631 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.105' to each side of the equation. 3.105 + -3.105 + x = 3.404550631 + -3.105 Combine like terms: 3.105 + -3.105 = 0.000 0.000 + x = 3.404550631 + -3.105 x = 3.404550631 + -3.105 Combine like terms: 3.404550631 + -3.105 = 0.299550631 x = 0.299550631 Simplifying x = 0.299550631Subproblem 2
x + 3.105 = -3.404550631 Simplifying x + 3.105 = -3.404550631 Reorder the terms: 3.105 + x = -3.404550631 Solving 3.105 + x = -3.404550631 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.105' to each side of the equation. 3.105 + -3.105 + x = -3.404550631 + -3.105 Combine like terms: 3.105 + -3.105 = 0.000 0.000 + x = -3.404550631 + -3.105 x = -3.404550631 + -3.105 Combine like terms: -3.404550631 + -3.105 = -6.509550631 x = -6.509550631 Simplifying x = -6.509550631Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.299550631, -6.509550631}
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