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Simplifying 2x2 + 34x + 11 = 0 Reorder the terms: 11 + 34x + 2x2 = 0 Solving 11 + 34x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 5.5 + 17x + x2 = 0 Move the constant term to the right: Add '-5.5' to each side of the equation. 5.5 + 17x + -5.5 + x2 = 0 + -5.5 Reorder the terms: 5.5 + -5.5 + 17x + x2 = 0 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + 17x + x2 = 0 + -5.5 17x + x2 = 0 + -5.5 Combine like terms: 0 + -5.5 = -5.5 17x + x2 = -5.5 The x term is 17x. Take half its coefficient (8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. 17x + 72.25 + x2 = -5.5 + 72.25 Reorder the terms: 72.25 + 17x + x2 = -5.5 + 72.25 Combine like terms: -5.5 + 72.25 = 66.75 72.25 + 17x + x2 = 66.75 Factor a perfect square on the left side: (x + 8.5)(x + 8.5) = 66.75 Calculate the square root of the right side: 8.170067319 Break this problem into two subproblems by setting (x + 8.5) equal to 8.170067319 and -8.170067319.Subproblem 1
x + 8.5 = 8.170067319 Simplifying x + 8.5 = 8.170067319 Reorder the terms: 8.5 + x = 8.170067319 Solving 8.5 + x = 8.170067319 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = 8.170067319 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = 8.170067319 + -8.5 x = 8.170067319 + -8.5 Combine like terms: 8.170067319 + -8.5 = -0.329932681 x = -0.329932681 Simplifying x = -0.329932681Subproblem 2
x + 8.5 = -8.170067319 Simplifying x + 8.5 = -8.170067319 Reorder the terms: 8.5 + x = -8.170067319 Solving 8.5 + x = -8.170067319 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = -8.170067319 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = -8.170067319 + -8.5 x = -8.170067319 + -8.5 Combine like terms: -8.170067319 + -8.5 = -16.670067319 x = -16.670067319 Simplifying x = -16.670067319Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.329932681, -16.670067319}
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