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Simplifying 0 = x2 + 50x + -200000 Reorder the terms: 0 = -200000 + 50x + x2 Solving 0 = -200000 + 50x + x2 Solving for variable 'x'. Combine like terms: 0 + 200000 = 200000 200000 + -50x + -1x2 = -200000 + 50x + x2 + 200000 + -50x + -1x2 Reorder the terms: 200000 + -50x + -1x2 = -200000 + 200000 + 50x + -50x + x2 + -1x2 Combine like terms: -200000 + 200000 = 0 200000 + -50x + -1x2 = 0 + 50x + -50x + x2 + -1x2 200000 + -50x + -1x2 = 50x + -50x + x2 + -1x2 Combine like terms: 50x + -50x = 0 200000 + -50x + -1x2 = 0 + x2 + -1x2 200000 + -50x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 200000 + -50x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -200000 + 50x + x2 = 0 Move the constant term to the right: Add '200000' to each side of the equation. -200000 + 50x + 200000 + x2 = 0 + 200000 Reorder the terms: -200000 + 200000 + 50x + x2 = 0 + 200000 Combine like terms: -200000 + 200000 = 0 0 + 50x + x2 = 0 + 200000 50x + x2 = 0 + 200000 Combine like terms: 0 + 200000 = 200000 50x + x2 = 200000 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 = 200000 + 625 Reorder the terms: 625 + 50x + x2 = 200000 + 625 Combine like terms: 200000 + 625 = 200625 625 + 50x + x2 = 200625 Factor a perfect square on the left side: (x + 25)(x + 25) = 200625 Calculate the square root of the right side: 447.911821679 Break this problem into two subproblems by setting (x + 25) equal to 447.911821679 and -447.911821679.Subproblem 1
x + 25 = 447.911821679 Simplifying x + 25 = 447.911821679 Reorder the terms: 25 + x = 447.911821679 Solving 25 + x = 447.911821679 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 = 447.911821679 + -25 Combine like terms: 25 + -25 = 0 0 + x = 447.911821679 + -25 x = 447.911821679 + -25 Combine like terms: 447.911821679 + -25 = 422.911821679 x = 422.911821679 Simplifying x = 422.911821679Subproblem 2
x + 25 = -447.911821679 Simplifying x + 25 = -447.911821679 Reorder the terms: 25 + x = -447.911821679 Solving 25 + x = -447.911821679 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 = -447.911821679 + -25 Combine like terms: 25 + -25 = 0 0 + x = -447.911821679 + -25 x = -447.911821679 + -25 Combine like terms: -447.911821679 + -25 = -472.911821679 x = -472.911821679 Simplifying x = -472.911821679Solution
The solution to the problem is based on the solutions from the subproblems. x = {422.911821679, -472.911821679}
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