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Simplifying x2 + 39x + 11 = 0 Reorder the terms: 11 + 39x + x2 = 0 Solving 11 + 39x + 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 + 39x + -11 + x2 = 0 + -11 Reorder the terms: 11 + -11 + 39x + x2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + 39x + x2 = 0 + -11 39x + x2 = 0 + -11 Combine like terms: 0 + -11 = -11 39x + x2 = -11 The x term is 39x. Take half its coefficient (19.5). Square it (380.25) and add it to both sides. Add '380.25' to each side of the equation. 39x + 380.25 + x2 = -11 + 380.25 Reorder the terms: 380.25 + 39x + x2 = -11 + 380.25 Combine like terms: -11 + 380.25 = 369.25 380.25 + 39x + x2 = 369.25 Factor a perfect square on the left side: (x + 19.5)(x + 19.5) = 369.25 Calculate the square root of the right side: 19.215878851 Break this problem into two subproblems by setting (x + 19.5) equal to 19.215878851 and -19.215878851.Subproblem 1
x + 19.5 = 19.215878851 Simplifying x + 19.5 = 19.215878851 Reorder the terms: 19.5 + x = 19.215878851 Solving 19.5 + x = 19.215878851 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-19.5' to each side of the equation. 19.5 + -19.5 + x = 19.215878851 + -19.5 Combine like terms: 19.5 + -19.5 = 0.0 0.0 + x = 19.215878851 + -19.5 x = 19.215878851 + -19.5 Combine like terms: 19.215878851 + -19.5 = -0.284121149 x = -0.284121149 Simplifying x = -0.284121149Subproblem 2
x + 19.5 = -19.215878851 Simplifying x + 19.5 = -19.215878851 Reorder the terms: 19.5 + x = -19.215878851 Solving 19.5 + x = -19.215878851 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-19.5' to each side of the equation. 19.5 + -19.5 + x = -19.215878851 + -19.5 Combine like terms: 19.5 + -19.5 = 0.0 0.0 + x = -19.215878851 + -19.5 x = -19.215878851 + -19.5 Combine like terms: -19.215878851 + -19.5 = -38.715878851 x = -38.715878851 Simplifying x = -38.715878851Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.284121149, -38.715878851}
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