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Simplifying x2 + 55x + -200 = 0 Reorder the terms: -200 + 55x + x2 = 0 Solving -200 + 55x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '200' to each side of the equation. -200 + 55x + 200 + x2 = 0 + 200 Reorder the terms: -200 + 200 + 55x + x2 = 0 + 200 Combine like terms: -200 + 200 = 0 0 + 55x + x2 = 0 + 200 55x + x2 = 0 + 200 Combine like terms: 0 + 200 = 200 55x + x2 = 200 The x term is 55x. Take half its coefficient (27.5). Square it (756.25) and add it to both sides. Add '756.25' to each side of the equation. 55x + 756.25 + x2 = 200 + 756.25 Reorder the terms: 756.25 + 55x + x2 = 200 + 756.25 Combine like terms: 200 + 756.25 = 956.25 756.25 + 55x + x2 = 956.25 Factor a perfect square on the left side: (x + 27.5)(x + 27.5) = 956.25 Calculate the square root of the right side: 30.923292192 Break this problem into two subproblems by setting (x + 27.5) equal to 30.923292192 and -30.923292192.Subproblem 1
x + 27.5 = 30.923292192 Simplifying x + 27.5 = 30.923292192 Reorder the terms: 27.5 + x = 30.923292192 Solving 27.5 + x = 30.923292192 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-27.5' to each side of the equation. 27.5 + -27.5 + x = 30.923292192 + -27.5 Combine like terms: 27.5 + -27.5 = 0.0 0.0 + x = 30.923292192 + -27.5 x = 30.923292192 + -27.5 Combine like terms: 30.923292192 + -27.5 = 3.423292192 x = 3.423292192 Simplifying x = 3.423292192Subproblem 2
x + 27.5 = -30.923292192 Simplifying x + 27.5 = -30.923292192 Reorder the terms: 27.5 + x = -30.923292192 Solving 27.5 + x = -30.923292192 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-27.5' to each side of the equation. 27.5 + -27.5 + x = -30.923292192 + -27.5 Combine like terms: 27.5 + -27.5 = 0.0 0.0 + x = -30.923292192 + -27.5 x = -30.923292192 + -27.5 Combine like terms: -30.923292192 + -27.5 = -58.423292192 x = -58.423292192 Simplifying x = -58.423292192Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.423292192, -58.423292192}
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