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Simplifying x2 + 19x + 11 = 0 Reorder the terms: 11 + 19x + x2 = 0 Solving 11 + 19x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-11' to each side of the equation. 11 + 19x + -11 + x2 = 0 + -11 Reorder the terms: 11 + -11 + 19x + x2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + 19x + x2 = 0 + -11 19x + x2 = 0 + -11 Combine like terms: 0 + -11 = -11 19x + x2 = -11 The x term is 19x. Take half its coefficient (9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. 19x + 90.25 + x2 = -11 + 90.25 Reorder the terms: 90.25 + 19x + x2 = -11 + 90.25 Combine like terms: -11 + 90.25 = 79.25 90.25 + 19x + x2 = 79.25 Factor a perfect square on the left side: (x + 9.5)(x + 9.5) = 79.25 Calculate the square root of the right side: 8.902246907 Break this problem into two subproblems by setting (x + 9.5) equal to 8.902246907 and -8.902246907.Subproblem 1
x + 9.5 = 8.902246907 Simplifying x + 9.5 = 8.902246907 Reorder the terms: 9.5 + x = 8.902246907 Solving 9.5 + x = 8.902246907 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + x = 8.902246907 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = 8.902246907 + -9.5 x = 8.902246907 + -9.5 Combine like terms: 8.902246907 + -9.5 = -0.597753093 x = -0.597753093 Simplifying x = -0.597753093Subproblem 2
x + 9.5 = -8.902246907 Simplifying x + 9.5 = -8.902246907 Reorder the terms: 9.5 + x = -8.902246907 Solving 9.5 + x = -8.902246907 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + x = -8.902246907 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = -8.902246907 + -9.5 x = -8.902246907 + -9.5 Combine like terms: -8.902246907 + -9.5 = -18.402246907 x = -18.402246907 Simplifying x = -18.402246907Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.597753093, -18.402246907}
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