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Simplifying x2 + -111x + -666 = 0 Reorder the terms: -666 + -111x + x2 = 0 Solving -666 + -111x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '666' to each side of the equation. -666 + -111x + 666 + x2 = 0 + 666 Reorder the terms: -666 + 666 + -111x + x2 = 0 + 666 Combine like terms: -666 + 666 = 0 0 + -111x + x2 = 0 + 666 -111x + x2 = 0 + 666 Combine like terms: 0 + 666 = 666 -111x + x2 = 666 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 = 666 + 3080.25 Reorder the terms: 3080.25 + -111x + x2 = 666 + 3080.25 Combine like terms: 666 + 3080.25 = 3746.25 3080.25 + -111x + x2 = 3746.25 Factor a perfect square on the left side: (x + -55.5)(x + -55.5) = 3746.25 Calculate the square root of the right side: 61.206617289 Break this problem into two subproblems by setting (x + -55.5) equal to 61.206617289 and -61.206617289.Subproblem 1
x + -55.5 = 61.206617289 Simplifying x + -55.5 = 61.206617289 Reorder the terms: -55.5 + x = 61.206617289 Solving -55.5 + x = 61.206617289 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 = 61.206617289 + 55.5 Combine like terms: -55.5 + 55.5 = 0.0 0.0 + x = 61.206617289 + 55.5 x = 61.206617289 + 55.5 Combine like terms: 61.206617289 + 55.5 = 116.706617289 x = 116.706617289 Simplifying x = 116.706617289Subproblem 2
x + -55.5 = -61.206617289 Simplifying x + -55.5 = -61.206617289 Reorder the terms: -55.5 + x = -61.206617289 Solving -55.5 + x = -61.206617289 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 = -61.206617289 + 55.5 Combine like terms: -55.5 + 55.5 = 0.0 0.0 + x = -61.206617289 + 55.5 x = -61.206617289 + 55.5 Combine like terms: -61.206617289 + 55.5 = -5.706617289 x = -5.706617289 Simplifying x = -5.706617289Solution
The solution to the problem is based on the solutions from the subproblems. x = {116.706617289, -5.706617289}
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