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Simplifying 2x2 + 11x = 16 Reorder the terms: 11x + 2x2 = 16 Solving 11x + 2x2 = 16 Solving for variable 'x'. Reorder the terms: -16 + 11x + 2x2 = 16 + -16 Combine like terms: 16 + -16 = 0 -16 + 11x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -8 + 5.5x + x2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + 5.5x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + 5.5x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 5.5x + x2 = 0 + 8 5.5x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 5.5x + x2 = 8 The x term is 5.5x. Take half its coefficient (2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. 5.5x + 7.5625 + x2 = 8 + 7.5625 Reorder the terms: 7.5625 + 5.5x + x2 = 8 + 7.5625 Combine like terms: 8 + 7.5625 = 15.5625 7.5625 + 5.5x + x2 = 15.5625 Factor a perfect square on the left side: (x + 2.75)(x + 2.75) = 15.5625 Calculate the square root of the right side: 3.94493346 Break this problem into two subproblems by setting (x + 2.75) equal to 3.94493346 and -3.94493346.Subproblem 1
x + 2.75 = 3.94493346 Simplifying x + 2.75 = 3.94493346 Reorder the terms: 2.75 + x = 3.94493346 Solving 2.75 + x = 3.94493346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = 3.94493346 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = 3.94493346 + -2.75 x = 3.94493346 + -2.75 Combine like terms: 3.94493346 + -2.75 = 1.19493346 x = 1.19493346 Simplifying x = 1.19493346Subproblem 2
x + 2.75 = -3.94493346 Simplifying x + 2.75 = -3.94493346 Reorder the terms: 2.75 + x = -3.94493346 Solving 2.75 + x = -3.94493346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = -3.94493346 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = -3.94493346 + -2.75 x = -3.94493346 + -2.75 Combine like terms: -3.94493346 + -2.75 = -6.69493346 x = -6.69493346 Simplifying x = -6.69493346Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.19493346, -6.69493346}
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