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Simplifying X2 + -1X = 366 Reorder the terms: -1X + X2 = 366 Solving -1X + X2 = 366 Solving for variable 'X'. Reorder the terms: -366 + -1X + X2 = 366 + -366 Combine like terms: 366 + -366 = 0 -366 + -1X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '366' to each side of the equation. -366 + -1X + 366 + X2 = 0 + 366 Reorder the terms: -366 + 366 + -1X + X2 = 0 + 366 Combine like terms: -366 + 366 = 0 0 + -1X + X2 = 0 + 366 -1X + X2 = 0 + 366 Combine like terms: 0 + 366 = 366 -1X + X2 = 366 The X term is -1X. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1X + 0.25 + X2 = 366 + 0.25 Reorder the terms: 0.25 + -1X + X2 = 366 + 0.25 Combine like terms: 366 + 0.25 = 366.25 0.25 + -1X + X2 = 366.25 Factor a perfect square on the left side: (X + -0.5)(X + -0.5) = 366.25 Calculate the square root of the right side: 19.137659209 Break this problem into two subproblems by setting (X + -0.5) equal to 19.137659209 and -19.137659209.Subproblem 1
X + -0.5 = 19.137659209 Simplifying X + -0.5 = 19.137659209 Reorder the terms: -0.5 + X = 19.137659209 Solving -0.5 + X = 19.137659209 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + X = 19.137659209 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + X = 19.137659209 + 0.5 X = 19.137659209 + 0.5 Combine like terms: 19.137659209 + 0.5 = 19.637659209 X = 19.637659209 Simplifying X = 19.637659209Subproblem 2
X + -0.5 = -19.137659209 Simplifying X + -0.5 = -19.137659209 Reorder the terms: -0.5 + X = -19.137659209 Solving -0.5 + X = -19.137659209 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + X = -19.137659209 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + X = -19.137659209 + 0.5 X = -19.137659209 + 0.5 Combine like terms: -19.137659209 + 0.5 = -18.637659209 X = -18.637659209 Simplifying X = -18.637659209Solution
The solution to the problem is based on the solutions from the subproblems. X = {19.637659209, -18.637659209}
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