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Simplifying 2x2 + 17x + 11 = 0 Reorder the terms: 11 + 17x + 2x2 = 0 Solving 11 + 17x + 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 + 8.5x + x2 = 0 Move the constant term to the right: Add '-5.5' to each side of the equation. 5.5 + 8.5x + -5.5 + x2 = 0 + -5.5 Reorder the terms: 5.5 + -5.5 + 8.5x + x2 = 0 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + 8.5x + x2 = 0 + -5.5 8.5x + x2 = 0 + -5.5 Combine like terms: 0 + -5.5 = -5.5 8.5x + x2 = -5.5 The x term is 8.5x. Take half its coefficient (4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. 8.5x + 18.0625 + x2 = -5.5 + 18.0625 Reorder the terms: 18.0625 + 8.5x + x2 = -5.5 + 18.0625 Combine like terms: -5.5 + 18.0625 = 12.5625 18.0625 + 8.5x + x2 = 12.5625 Factor a perfect square on the left side: (x + 4.25)(x + 4.25) = 12.5625 Calculate the square root of the right side: 3.54436172 Break this problem into two subproblems by setting (x + 4.25) equal to 3.54436172 and -3.54436172.Subproblem 1
x + 4.25 = 3.54436172 Simplifying x + 4.25 = 3.54436172 Reorder the terms: 4.25 + x = 3.54436172 Solving 4.25 + x = 3.54436172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + x = 3.54436172 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = 3.54436172 + -4.25 x = 3.54436172 + -4.25 Combine like terms: 3.54436172 + -4.25 = -0.70563828 x = -0.70563828 Simplifying x = -0.70563828Subproblem 2
x + 4.25 = -3.54436172 Simplifying x + 4.25 = -3.54436172 Reorder the terms: 4.25 + x = -3.54436172 Solving 4.25 + x = -3.54436172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + x = -3.54436172 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = -3.54436172 + -4.25 x = -3.54436172 + -4.25 Combine like terms: -3.54436172 + -4.25 = -7.79436172 x = -7.79436172 Simplifying x = -7.79436172Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.70563828, -7.79436172}
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