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Simplifying 11x = x2 + -40 Reorder the terms: 11x = -40 + x2 Solving 11x = -40 + x2 Solving for variable 'x'. Reorder the terms: 40 + 11x + -1x2 = -40 + x2 + 40 + -1x2 Reorder the terms: 40 + 11x + -1x2 = -40 + 40 + x2 + -1x2 Combine like terms: -40 + 40 = 0 40 + 11x + -1x2 = 0 + x2 + -1x2 40 + 11x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 40 + 11x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -40 + -11x + x2 = 0 Move the constant term to the right: Add '40' to each side of the equation. -40 + -11x + 40 + x2 = 0 + 40 Reorder the terms: -40 + 40 + -11x + x2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + -11x + x2 = 0 + 40 -11x + x2 = 0 + 40 Combine like terms: 0 + 40 = 40 -11x + x2 = 40 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 = 40 + 30.25 Reorder the terms: 30.25 + -11x + x2 = 40 + 30.25 Combine like terms: 40 + 30.25 = 70.25 30.25 + -11x + x2 = 70.25 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 70.25 Calculate the square root of the right side: 8.381527307 Break this problem into two subproblems by setting (x + -5.5) equal to 8.381527307 and -8.381527307.Subproblem 1
x + -5.5 = 8.381527307 Simplifying x + -5.5 = 8.381527307 Reorder the terms: -5.5 + x = 8.381527307 Solving -5.5 + x = 8.381527307 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 = 8.381527307 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 8.381527307 + 5.5 x = 8.381527307 + 5.5 Combine like terms: 8.381527307 + 5.5 = 13.881527307 x = 13.881527307 Simplifying x = 13.881527307Subproblem 2
x + -5.5 = -8.381527307 Simplifying x + -5.5 = -8.381527307 Reorder the terms: -5.5 + x = -8.381527307 Solving -5.5 + x = -8.381527307 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 = -8.381527307 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -8.381527307 + 5.5 x = -8.381527307 + 5.5 Combine like terms: -8.381527307 + 5.5 = -2.881527307 x = -2.881527307 Simplifying x = -2.881527307Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.881527307, -2.881527307}
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