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Simplifying -1x2 + -50x + 144 = 0 Reorder the terms: 144 + -50x + -1x2 = 0 Solving 144 + -50x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -144 + 50x + x2 = 0 Move the constant term to the right: Add '144' to each side of the equation. -144 + 50x + 144 + x2 = 0 + 144 Reorder the terms: -144 + 144 + 50x + x2 = 0 + 144 Combine like terms: -144 + 144 = 0 0 + 50x + x2 = 0 + 144 50x + x2 = 0 + 144 Combine like terms: 0 + 144 = 144 50x + x2 = 144 The x term is 50x. Take half its coefficient (25). Square it (625) and add it to both sides. Add '625' to each side of the equation. 50x + 625 + x2 = 144 + 625 Reorder the terms: 625 + 50x + x2 = 144 + 625 Combine like terms: 144 + 625 = 769 625 + 50x + x2 = 769 Factor a perfect square on the left side: (x + 25)(x + 25) = 769 Calculate the square root of the right side: 27.730849248 Break this problem into two subproblems by setting (x + 25) equal to 27.730849248 and -27.730849248.Subproblem 1
x + 25 = 27.730849248 Simplifying x + 25 = 27.730849248 Reorder the terms: 25 + x = 27.730849248 Solving 25 + x = 27.730849248 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + x = 27.730849248 + -25 Combine like terms: 25 + -25 = 0 0 + x = 27.730849248 + -25 x = 27.730849248 + -25 Combine like terms: 27.730849248 + -25 = 2.730849248 x = 2.730849248 Simplifying x = 2.730849248Subproblem 2
x + 25 = -27.730849248 Simplifying x + 25 = -27.730849248 Reorder the terms: 25 + x = -27.730849248 Solving 25 + x = -27.730849248 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + x = -27.730849248 + -25 Combine like terms: 25 + -25 = 0 0 + x = -27.730849248 + -25 x = -27.730849248 + -25 Combine like terms: -27.730849248 + -25 = -52.730849248 x = -52.730849248 Simplifying x = -52.730849248Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.730849248, -52.730849248}
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