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Simplifying X2 + -21X + 1 = 0 Reorder the terms: 1 + -21X + X2 = 0 Solving 1 + -21X + X2 = 0 Solving for variable 'X'. Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -21X + -1 + X2 = 0 + -1 Reorder the terms: 1 + -1 + -21X + X2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -21X + X2 = 0 + -1 -21X + X2 = 0 + -1 Combine like terms: 0 + -1 = -1 -21X + X2 = -1 The X term is -21X. Take half its coefficient (-10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. -21X + 110.25 + X2 = -1 + 110.25 Reorder the terms: 110.25 + -21X + X2 = -1 + 110.25 Combine like terms: -1 + 110.25 = 109.25 110.25 + -21X + X2 = 109.25 Factor a perfect square on the left side: (X + -10.5)(X + -10.5) = 109.25 Calculate the square root of the right side: 10.45227248 Break this problem into two subproblems by setting (X + -10.5) equal to 10.45227248 and -10.45227248.Subproblem 1
X + -10.5 = 10.45227248 Simplifying X + -10.5 = 10.45227248 Reorder the terms: -10.5 + X = 10.45227248 Solving -10.5 + X = 10.45227248 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + X = 10.45227248 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + X = 10.45227248 + 10.5 X = 10.45227248 + 10.5 Combine like terms: 10.45227248 + 10.5 = 20.95227248 X = 20.95227248 Simplifying X = 20.95227248Subproblem 2
X + -10.5 = -10.45227248 Simplifying X + -10.5 = -10.45227248 Reorder the terms: -10.5 + X = -10.45227248 Solving -10.5 + X = -10.45227248 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + X = -10.45227248 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + X = -10.45227248 + 10.5 X = -10.45227248 + 10.5 Combine like terms: -10.45227248 + 10.5 = 0.04772752 X = 0.04772752 Simplifying X = 0.04772752Solution
The solution to the problem is based on the solutions from the subproblems. X = {20.95227248, 0.04772752}
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