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Simplifying 14x2 + 600x + -1409 = 0 Reorder the terms: -1409 + 600x + 14x2 = 0 Solving -1409 + 600x + 14x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -100.6428571 + 42.85714286x + x2 = 0 Move the constant term to the right: Add '100.6428571' to each side of the equation. -100.6428571 + 42.85714286x + 100.6428571 + x2 = 0 + 100.6428571 Reorder the terms: -100.6428571 + 100.6428571 + 42.85714286x + x2 = 0 + 100.6428571 Combine like terms: -100.6428571 + 100.6428571 = 0.0000000 0.0000000 + 42.85714286x + x2 = 0 + 100.6428571 42.85714286x + x2 = 0 + 100.6428571 Combine like terms: 0 + 100.6428571 = 100.6428571 42.85714286x + x2 = 100.6428571 The x term is 42.85714286x. Take half its coefficient (21.42857143). Square it (459.1836735) and add it to both sides. Add '459.1836735' to each side of the equation. 42.85714286x + 459.1836735 + x2 = 100.6428571 + 459.1836735 Reorder the terms: 459.1836735 + 42.85714286x + x2 = 100.6428571 + 459.1836735 Combine like terms: 100.6428571 + 459.1836735 = 559.8265306 459.1836735 + 42.85714286x + x2 = 559.8265306 Factor a perfect square on the left side: (x + 21.42857143)(x + 21.42857143) = 559.8265306 Calculate the square root of the right side: 23.660653638 Break this problem into two subproblems by setting (x + 21.42857143) equal to 23.660653638 and -23.660653638.Subproblem 1
x + 21.42857143 = 23.660653638 Simplifying x + 21.42857143 = 23.660653638 Reorder the terms: 21.42857143 + x = 23.660653638 Solving 21.42857143 + x = 23.660653638 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-21.42857143' to each side of the equation. 21.42857143 + -21.42857143 + x = 23.660653638 + -21.42857143 Combine like terms: 21.42857143 + -21.42857143 = 0.00000000 0.00000000 + x = 23.660653638 + -21.42857143 x = 23.660653638 + -21.42857143 Combine like terms: 23.660653638 + -21.42857143 = 2.232082208 x = 2.232082208 Simplifying x = 2.232082208Subproblem 2
x + 21.42857143 = -23.660653638 Simplifying x + 21.42857143 = -23.660653638 Reorder the terms: 21.42857143 + x = -23.660653638 Solving 21.42857143 + x = -23.660653638 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-21.42857143' to each side of the equation. 21.42857143 + -21.42857143 + x = -23.660653638 + -21.42857143 Combine like terms: 21.42857143 + -21.42857143 = 0.00000000 0.00000000 + x = -23.660653638 + -21.42857143 x = -23.660653638 + -21.42857143 Combine like terms: -23.660653638 + -21.42857143 = -45.089225068 x = -45.089225068 Simplifying x = -45.089225068Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.232082208, -45.089225068}
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