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Simplifying x + 380 = x2 * 3 Reorder the terms: 380 + x = x2 * 3 Reorder the terms for easier multiplication: 380 + x = 3x2 Solving 380 + x = 3x2 Solving for variable 'x'. Combine like terms: 3x2 + -3x2 = 0 380 + x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -126.6666667 + -0.3333333333x + x2 = 0 Move the constant term to the right: Add '126.6666667' to each side of the equation. -126.6666667 + -0.3333333333x + 126.6666667 + x2 = 0 + 126.6666667 Reorder the terms: -126.6666667 + 126.6666667 + -0.3333333333x + x2 = 0 + 126.6666667 Combine like terms: -126.6666667 + 126.6666667 = 0.0000000 0.0000000 + -0.3333333333x + x2 = 0 + 126.6666667 -0.3333333333x + x2 = 0 + 126.6666667 Combine like terms: 0 + 126.6666667 = 126.6666667 -0.3333333333x + x2 = 126.6666667 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -0.3333333333x + 0.25 + x2 = 126.6666667 + 0.25 Reorder the terms: 0.25 + -0.3333333333x + x2 = 126.6666667 + 0.25 Combine like terms: 126.6666667 + 0.25 = 126.9166667 0.25 + -0.3333333333x + x2 = 126.9166667 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 126.9166667 Calculate the square root of the right side: 11.265729746 Break this problem into two subproblems by setting (x + 0.5) equal to 11.265729746 and -11.265729746.Subproblem 1
x + 0.5 = 11.265729746 Simplifying x + 0.5 = 11.265729746 Reorder the terms: 0.5 + x = 11.265729746 Solving 0.5 + x = 11.265729746 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 11.265729746 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 11.265729746 + -0.5 x = 11.265729746 + -0.5 Combine like terms: 11.265729746 + -0.5 = 10.765729746 x = 10.765729746 Simplifying x = 10.765729746Subproblem 2
x + 0.5 = -11.265729746 Simplifying x + 0.5 = -11.265729746 Reorder the terms: 0.5 + x = -11.265729746 Solving 0.5 + x = -11.265729746 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -11.265729746 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -11.265729746 + -0.5 x = -11.265729746 + -0.5 Combine like terms: -11.265729746 + -0.5 = -11.765729746 x = -11.765729746 Simplifying x = -11.765729746Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.765729746, -11.765729746}
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