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Simplifying 26 = X2 + 20X Reorder the terms: 26 = 20X + X2 Solving 26 = 20X + X2 Solving for variable 'X'. Reorder the terms: 26 + -20X + -1X2 = 20X + -20X + X2 + -1X2 Combine like terms: 20X + -20X = 0 26 + -20X + -1X2 = 0 + X2 + -1X2 26 + -20X + -1X2 = X2 + -1X2 Combine like terms: X2 + -1X2 = 0 26 + -20X + -1X2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -26 + 20X + X2 = 0 Move the constant term to the right: Add '26' to each side of the equation. -26 + 20X + 26 + X2 = 0 + 26 Reorder the terms: -26 + 26 + 20X + X2 = 0 + 26 Combine like terms: -26 + 26 = 0 0 + 20X + X2 = 0 + 26 20X + X2 = 0 + 26 Combine like terms: 0 + 26 = 26 20X + X2 = 26 The X term is 20X. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20X + 100 + X2 = 26 + 100 Reorder the terms: 100 + 20X + X2 = 26 + 100 Combine like terms: 26 + 100 = 126 100 + 20X + X2 = 126 Factor a perfect square on the left side: (X + 10)(X + 10) = 126 Calculate the square root of the right side: 11.22497216 Break this problem into two subproblems by setting (X + 10) equal to 11.22497216 and -11.22497216.Subproblem 1
X + 10 = 11.22497216 Simplifying X + 10 = 11.22497216 Reorder the terms: 10 + X = 11.22497216 Solving 10 + X = 11.22497216 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + X = 11.22497216 + -10 Combine like terms: 10 + -10 = 0 0 + X = 11.22497216 + -10 X = 11.22497216 + -10 Combine like terms: 11.22497216 + -10 = 1.22497216 X = 1.22497216 Simplifying X = 1.22497216Subproblem 2
X + 10 = -11.22497216 Simplifying X + 10 = -11.22497216 Reorder the terms: 10 + X = -11.22497216 Solving 10 + X = -11.22497216 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + X = -11.22497216 + -10 Combine like terms: 10 + -10 = 0 0 + X = -11.22497216 + -10 X = -11.22497216 + -10 Combine like terms: -11.22497216 + -10 = -21.22497216 X = -21.22497216 Simplifying X = -21.22497216Solution
The solution to the problem is based on the solutions from the subproblems. X = {1.22497216, -21.22497216}
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