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Simplifying 11x + 212 = x2 Reorder the terms: 212 + 11x = x2 Solving 212 + 11x = x2 Solving for variable 'x'. Combine like terms: x2 + -1x2 = 0 212 + 11x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -212 + -11x + x2 = 0 Move the constant term to the right: Add '212' to each side of the equation. -212 + -11x + 212 + x2 = 0 + 212 Reorder the terms: -212 + 212 + -11x + x2 = 0 + 212 Combine like terms: -212 + 212 = 0 0 + -11x + x2 = 0 + 212 -11x + x2 = 0 + 212 Combine like terms: 0 + 212 = 212 -11x + x2 = 212 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 = 212 + 30.25 Reorder the terms: 30.25 + -11x + x2 = 212 + 30.25 Combine like terms: 212 + 30.25 = 242.25 30.25 + -11x + x2 = 242.25 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 242.25 Calculate the square root of the right side: 15.564382416 Break this problem into two subproblems by setting (x + -5.5) equal to 15.564382416 and -15.564382416.Subproblem 1
x + -5.5 = 15.564382416 Simplifying x + -5.5 = 15.564382416 Reorder the terms: -5.5 + x = 15.564382416 Solving -5.5 + x = 15.564382416 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 = 15.564382416 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 15.564382416 + 5.5 x = 15.564382416 + 5.5 Combine like terms: 15.564382416 + 5.5 = 21.064382416 x = 21.064382416 Simplifying x = 21.064382416Subproblem 2
x + -5.5 = -15.564382416 Simplifying x + -5.5 = -15.564382416 Reorder the terms: -5.5 + x = -15.564382416 Solving -5.5 + x = -15.564382416 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 = -15.564382416 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -15.564382416 + 5.5 x = -15.564382416 + 5.5 Combine like terms: -15.564382416 + 5.5 = -10.064382416 x = -10.064382416 Simplifying x = -10.064382416Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.064382416, -10.064382416}
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