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Simplifying 11X2 + 11X + -26 = 0 Reorder the terms: -26 + 11X + 11X2 = 0 Solving -26 + 11X + 11X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -2.363636364 + X + X2 = 0 Move the constant term to the right: Add '2.363636364' to each side of the equation. -2.363636364 + X + 2.363636364 + X2 = 0 + 2.363636364 Reorder the terms: -2.363636364 + 2.363636364 + X + X2 = 0 + 2.363636364 Combine like terms: -2.363636364 + 2.363636364 = 0.000000000 0.000000000 + X + X2 = 0 + 2.363636364 X + X2 = 0 + 2.363636364 Combine like terms: 0 + 2.363636364 = 2.363636364 X + X2 = 2.363636364 The X term is X. 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. + 0.25 + X2 = 2.363636364 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + X2 = 2.363636364 + 0.25 Combine like terms: 2.363636364 + 0.25 = 2.613636364 1.25 + X2 = 2.613636364 Factor a perfect square on the left side: (X + 0.5)(X + 0.5) = 2.613636364 Calculate the square root of the right side: 1.616674477 Break this problem into two subproblems by setting (X + 0.5) equal to 1.616674477 and -1.616674477.Subproblem 1
X + 0.5 = 1.616674477 Simplifying X + 0.5 = 1.616674477 Reorder the terms: 0.5 + X = 1.616674477 Solving 0.5 + X = 1.616674477 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 = 1.616674477 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + X = 1.616674477 + -0.5 X = 1.616674477 + -0.5 Combine like terms: 1.616674477 + -0.5 = 1.116674477 X = 1.116674477 Simplifying X = 1.116674477Subproblem 2
X + 0.5 = -1.616674477 Simplifying X + 0.5 = -1.616674477 Reorder the terms: 0.5 + X = -1.616674477 Solving 0.5 + X = -1.616674477 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 = -1.616674477 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + X = -1.616674477 + -0.5 X = -1.616674477 + -0.5 Combine like terms: -1.616674477 + -0.5 = -2.116674477 X = -2.116674477 Simplifying X = -2.116674477Solution
The solution to the problem is based on the solutions from the subproblems. X = {1.116674477, -2.116674477}
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