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Simplifying X2 + -22X + 75 = 0 Reorder the terms: 75 + -22X + X2 = 0 Solving 75 + -22X + X2 = 0 Solving for variable 'X'. Begin completing the square. Move the constant term to the right: Add '-75' to each side of the equation. 75 + -22X + -75 + X2 = 0 + -75 Reorder the terms: 75 + -75 + -22X + X2 = 0 + -75 Combine like terms: 75 + -75 = 0 0 + -22X + X2 = 0 + -75 -22X + X2 = 0 + -75 Combine like terms: 0 + -75 = -75 -22X + X2 = -75 The X term is -22X. Take half its coefficient (-11). Square it (121) and add it to both sides. Add '121' to each side of the equation. -22X + 121 + X2 = -75 + 121 Reorder the terms: 121 + -22X + X2 = -75 + 121 Combine like terms: -75 + 121 = 46 121 + -22X + X2 = 46 Factor a perfect square on the left side: (X + -11)(X + -11) = 46 Calculate the square root of the right side: 6.782329983 Break this problem into two subproblems by setting (X + -11) equal to 6.782329983 and -6.782329983.Subproblem 1
X + -11 = 6.782329983 Simplifying X + -11 = 6.782329983 Reorder the terms: -11 + X = 6.782329983 Solving -11 + X = 6.782329983 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + X = 6.782329983 + 11 Combine like terms: -11 + 11 = 0 0 + X = 6.782329983 + 11 X = 6.782329983 + 11 Combine like terms: 6.782329983 + 11 = 17.782329983 X = 17.782329983 Simplifying X = 17.782329983Subproblem 2
X + -11 = -6.782329983 Simplifying X + -11 = -6.782329983 Reorder the terms: -11 + X = -6.782329983 Solving -11 + X = -6.782329983 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + X = -6.782329983 + 11 Combine like terms: -11 + 11 = 0 0 + X = -6.782329983 + 11 X = -6.782329983 + 11 Combine like terms: -6.782329983 + 11 = 4.217670017 X = 4.217670017 Simplifying X = 4.217670017Solution
The solution to the problem is based on the solutions from the subproblems. X = {17.782329983, 4.217670017}
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