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Simplifying x2 + -111x + -56 = 0 Reorder the terms: -56 + -111x + x2 = 0 Solving -56 + -111x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '56' to each side of the equation. -56 + -111x + 56 + x2 = 0 + 56 Reorder the terms: -56 + 56 + -111x + x2 = 0 + 56 Combine like terms: -56 + 56 = 0 0 + -111x + x2 = 0 + 56 -111x + x2 = 0 + 56 Combine like terms: 0 + 56 = 56 -111x + x2 = 56 The x term is -111x. Take half its coefficient (-55.5). Square it (3080.25) and add it to both sides. Add '3080.25' to each side of the equation. -111x + 3080.25 + x2 = 56 + 3080.25 Reorder the terms: 3080.25 + -111x + x2 = 56 + 3080.25 Combine like terms: 56 + 3080.25 = 3136.25 3080.25 + -111x + x2 = 3136.25 Factor a perfect square on the left side: (x + -55.5)(x + -55.5) = 3136.25 Calculate the square root of the right side: 56.002232098 Break this problem into two subproblems by setting (x + -55.5) equal to 56.002232098 and -56.002232098.Subproblem 1
x + -55.5 = 56.002232098 Simplifying x + -55.5 = 56.002232098 Reorder the terms: -55.5 + x = 56.002232098 Solving -55.5 + x = 56.002232098 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '55.5' to each side of the equation. -55.5 + 55.5 + x = 56.002232098 + 55.5 Combine like terms: -55.5 + 55.5 = 0.0 0.0 + x = 56.002232098 + 55.5 x = 56.002232098 + 55.5 Combine like terms: 56.002232098 + 55.5 = 111.502232098 x = 111.502232098 Simplifying x = 111.502232098Subproblem 2
x + -55.5 = -56.002232098 Simplifying x + -55.5 = -56.002232098 Reorder the terms: -55.5 + x = -56.002232098 Solving -55.5 + x = -56.002232098 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '55.5' to each side of the equation. -55.5 + 55.5 + x = -56.002232098 + 55.5 Combine like terms: -55.5 + 55.5 = 0.0 0.0 + x = -56.002232098 + 55.5 x = -56.002232098 + 55.5 Combine like terms: -56.002232098 + 55.5 = -0.502232098 x = -0.502232098 Simplifying x = -0.502232098Solution
The solution to the problem is based on the solutions from the subproblems. x = {111.502232098, -0.502232098}
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