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Simplifying x2 + -200x + 4805.34 = 0 Reorder the terms: 4805.34 + -200x + x2 = 0 Solving 4805.34 + -200x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-4805.34' to each side of the equation. 4805.34 + -200x + -4805.34 + x2 = 0 + -4805.34 Reorder the terms: 4805.34 + -4805.34 + -200x + x2 = 0 + -4805.34 Combine like terms: 4805.34 + -4805.34 = 0.00 0.00 + -200x + x2 = 0 + -4805.34 -200x + x2 = 0 + -4805.34 Combine like terms: 0 + -4805.34 = -4805.34 -200x + x2 = -4805.34 The x term is -200x. Take half its coefficient (-100). Square it (10000) and add it to both sides. Add '10000' to each side of the equation. -200x + 10000 + x2 = -4805.34 + 10000 Reorder the terms: 10000 + -200x + x2 = -4805.34 + 10000 Combine like terms: -4805.34 + 10000 = 5194.66 10000 + -200x + x2 = 5194.66 Factor a perfect square on the left side: (x + -100)(x + -100) = 5194.66 Calculate the square root of the right side: 72.073989761 Break this problem into two subproblems by setting (x + -100) equal to 72.073989761 and -72.073989761.Subproblem 1
x + -100 = 72.073989761 Simplifying x + -100 = 72.073989761 Reorder the terms: -100 + x = 72.073989761 Solving -100 + x = 72.073989761 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + x = 72.073989761 + 100 Combine like terms: -100 + 100 = 0 0 + x = 72.073989761 + 100 x = 72.073989761 + 100 Combine like terms: 72.073989761 + 100 = 172.073989761 x = 172.073989761 Simplifying x = 172.073989761Subproblem 2
x + -100 = -72.073989761 Simplifying x + -100 = -72.073989761 Reorder the terms: -100 + x = -72.073989761 Solving -100 + x = -72.073989761 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + x = -72.073989761 + 100 Combine like terms: -100 + 100 = 0 0 + x = -72.073989761 + 100 x = -72.073989761 + 100 Combine like terms: -72.073989761 + 100 = 27.926010239 x = 27.926010239 Simplifying x = 27.926010239Solution
The solution to the problem is based on the solutions from the subproblems. x = {172.073989761, 27.926010239}
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