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Simplifying 2x2 + 23x = 11 Reorder the terms: 23x + 2x2 = 11 Solving 23x + 2x2 = 11 Solving for variable 'x'. Reorder the terms: -11 + 23x + 2x2 = 11 + -11 Combine like terms: 11 + -11 = 0 -11 + 23x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -5.5 + 11.5x + x2 = 0 Move the constant term to the right: Add '5.5' to each side of the equation. -5.5 + 11.5x + 5.5 + x2 = 0 + 5.5 Reorder the terms: -5.5 + 5.5 + 11.5x + x2 = 0 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + 11.5x + x2 = 0 + 5.5 11.5x + x2 = 0 + 5.5 Combine like terms: 0 + 5.5 = 5.5 11.5x + x2 = 5.5 The x term is 11.5x. Take half its coefficient (5.75). Square it (33.0625) and add it to both sides. Add '33.0625' to each side of the equation. 11.5x + 33.0625 + x2 = 5.5 + 33.0625 Reorder the terms: 33.0625 + 11.5x + x2 = 5.5 + 33.0625 Combine like terms: 5.5 + 33.0625 = 38.5625 33.0625 + 11.5x + x2 = 38.5625 Factor a perfect square on the left side: (x + 5.75)(x + 5.75) = 38.5625 Calculate the square root of the right side: 6.209871174 Break this problem into two subproblems by setting (x + 5.75) equal to 6.209871174 and -6.209871174.Subproblem 1
x + 5.75 = 6.209871174 Simplifying x + 5.75 = 6.209871174 Reorder the terms: 5.75 + x = 6.209871174 Solving 5.75 + x = 6.209871174 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.75' to each side of the equation. 5.75 + -5.75 + x = 6.209871174 + -5.75 Combine like terms: 5.75 + -5.75 = 0.00 0.00 + x = 6.209871174 + -5.75 x = 6.209871174 + -5.75 Combine like terms: 6.209871174 + -5.75 = 0.459871174 x = 0.459871174 Simplifying x = 0.459871174Subproblem 2
x + 5.75 = -6.209871174 Simplifying x + 5.75 = -6.209871174 Reorder the terms: 5.75 + x = -6.209871174 Solving 5.75 + x = -6.209871174 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.75' to each side of the equation. 5.75 + -5.75 + x = -6.209871174 + -5.75 Combine like terms: 5.75 + -5.75 = 0.00 0.00 + x = -6.209871174 + -5.75 x = -6.209871174 + -5.75 Combine like terms: -6.209871174 + -5.75 = -11.959871174 x = -11.959871174 Simplifying x = -11.959871174Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.459871174, -11.959871174}
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