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Simplifying X + 1 = X2 + -10X + 26 Reorder the terms: 1 + X = X2 + -10X + 26 Reorder the terms: 1 + X = 26 + -10X + X2 Solving 1 + X = 26 + -10X + X2 Solving for variable 'X'. Reorder the terms: 1 + -26 + X + 10X + -1X2 = 26 + -10X + X2 + -26 + 10X + -1X2 Combine like terms: 1 + -26 = -25 -25 + X + 10X + -1X2 = 26 + -10X + X2 + -26 + 10X + -1X2 Combine like terms: X + 10X = 11X -25 + 11X + -1X2 = 26 + -10X + X2 + -26 + 10X + -1X2 Reorder the terms: -25 + 11X + -1X2 = 26 + -26 + -10X + 10X + X2 + -1X2 Combine like terms: 26 + -26 = 0 -25 + 11X + -1X2 = 0 + -10X + 10X + X2 + -1X2 -25 + 11X + -1X2 = -10X + 10X + X2 + -1X2 Combine like terms: -10X + 10X = 0 -25 + 11X + -1X2 = 0 + X2 + -1X2 -25 + 11X + -1X2 = X2 + -1X2 Combine like terms: X2 + -1X2 = 0 -25 + 11X + -1X2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 25 + -11X + X2 = 0 Move the constant term to the right: Add '-25' to each side of the equation. 25 + -11X + -25 + X2 = 0 + -25 Reorder the terms: 25 + -25 + -11X + X2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -11X + X2 = 0 + -25 -11X + X2 = 0 + -25 Combine like terms: 0 + -25 = -25 -11X + X2 = -25 The X term is -11X. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11X + 30.25 + X2 = -25 + 30.25 Reorder the terms: 30.25 + -11X + X2 = -25 + 30.25 Combine like terms: -25 + 30.25 = 5.25 30.25 + -11X + X2 = 5.25 Factor a perfect square on the left side: (X + -5.5)(X + -5.5) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (X + -5.5) equal to 2.291287847 and -2.291287847.Subproblem 1
X + -5.5 = 2.291287847 Simplifying X + -5.5 = 2.291287847 Reorder the terms: -5.5 + X = 2.291287847 Solving -5.5 + X = 2.291287847 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + X = 2.291287847 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + X = 2.291287847 + 5.5 X = 2.291287847 + 5.5 Combine like terms: 2.291287847 + 5.5 = 7.791287847 X = 7.791287847 Simplifying X = 7.791287847Subproblem 2
X + -5.5 = -2.291287847 Simplifying X + -5.5 = -2.291287847 Reorder the terms: -5.5 + X = -2.291287847 Solving -5.5 + X = -2.291287847 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + X = -2.291287847 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + X = -2.291287847 + 5.5 X = -2.291287847 + 5.5 Combine like terms: -2.291287847 + 5.5 = 3.208712153 X = 3.208712153 Simplifying X = 3.208712153Solution
The solution to the problem is based on the solutions from the subproblems. X = {7.791287847, 3.208712153}
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