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Simplifying 13x2 + -250x + 600 = 0 Reorder the terms: 600 + -250x + 13x2 = 0 Solving 600 + -250x + 13x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. 46.15384615 + -19.23076923x + x2 = 0 Move the constant term to the right: Add '-46.15384615' to each side of the equation. 46.15384615 + -19.23076923x + -46.15384615 + x2 = 0 + -46.15384615 Reorder the terms: 46.15384615 + -46.15384615 + -19.23076923x + x2 = 0 + -46.15384615 Combine like terms: 46.15384615 + -46.15384615 = 0.00000000 0.00000000 + -19.23076923x + x2 = 0 + -46.15384615 -19.23076923x + x2 = 0 + -46.15384615 Combine like terms: 0 + -46.15384615 = -46.15384615 -19.23076923x + x2 = -46.15384615 The x term is -19.23076923x. Take half its coefficient (-9.615384615). Square it (92.45562129) and add it to both sides. Add '92.45562129' to each side of the equation. -19.23076923x + 92.45562129 + x2 = -46.15384615 + 92.45562129 Reorder the terms: 92.45562129 + -19.23076923x + x2 = -46.15384615 + 92.45562129 Combine like terms: -46.15384615 + 92.45562129 = 46.30177514 92.45562129 + -19.23076923x + x2 = 46.30177514 Factor a perfect square on the left side: (x + -9.615384615)(x + -9.615384615) = 46.30177514 Calculate the square root of the right side: 6.804540774 Break this problem into two subproblems by setting (x + -9.615384615) equal to 6.804540774 and -6.804540774.Subproblem 1
x + -9.615384615 = 6.804540774 Simplifying x + -9.615384615 = 6.804540774 Reorder the terms: -9.615384615 + x = 6.804540774 Solving -9.615384615 + x = 6.804540774 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.615384615' to each side of the equation. -9.615384615 + 9.615384615 + x = 6.804540774 + 9.615384615 Combine like terms: -9.615384615 + 9.615384615 = 0.000000000 0.000000000 + x = 6.804540774 + 9.615384615 x = 6.804540774 + 9.615384615 Combine like terms: 6.804540774 + 9.615384615 = 16.419925389 x = 16.419925389 Simplifying x = 16.419925389Subproblem 2
x + -9.615384615 = -6.804540774 Simplifying x + -9.615384615 = -6.804540774 Reorder the terms: -9.615384615 + x = -6.804540774 Solving -9.615384615 + x = -6.804540774 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.615384615' to each side of the equation. -9.615384615 + 9.615384615 + x = -6.804540774 + 9.615384615 Combine like terms: -9.615384615 + 9.615384615 = 0.000000000 0.000000000 + x = -6.804540774 + 9.615384615 x = -6.804540774 + 9.615384615 Combine like terms: -6.804540774 + 9.615384615 = 2.810843841 x = 2.810843841 Simplifying x = 2.810843841Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.419925389, 2.810843841}
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