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Simplifying x2 + 29x + 19 = 0 Reorder the terms: 19 + 29x + x2 = 0 Solving 19 + 29x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-19' to each side of the equation. 19 + 29x + -19 + x2 = 0 + -19 Reorder the terms: 19 + -19 + 29x + x2 = 0 + -19 Combine like terms: 19 + -19 = 0 0 + 29x + x2 = 0 + -19 29x + x2 = 0 + -19 Combine like terms: 0 + -19 = -19 29x + x2 = -19 The x term is 29x. Take half its coefficient (14.5). Square it (210.25) and add it to both sides. Add '210.25' to each side of the equation. 29x + 210.25 + x2 = -19 + 210.25 Reorder the terms: 210.25 + 29x + x2 = -19 + 210.25 Combine like terms: -19 + 210.25 = 191.25 210.25 + 29x + x2 = 191.25 Factor a perfect square on the left side: (x + 14.5)(x + 14.5) = 191.25 Calculate the square root of the right side: 13.829316686 Break this problem into two subproblems by setting (x + 14.5) equal to 13.829316686 and -13.829316686.Subproblem 1
x + 14.5 = 13.829316686 Simplifying x + 14.5 = 13.829316686 Reorder the terms: 14.5 + x = 13.829316686 Solving 14.5 + x = 13.829316686 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14.5' to each side of the equation. 14.5 + -14.5 + x = 13.829316686 + -14.5 Combine like terms: 14.5 + -14.5 = 0.0 0.0 + x = 13.829316686 + -14.5 x = 13.829316686 + -14.5 Combine like terms: 13.829316686 + -14.5 = -0.670683314 x = -0.670683314 Simplifying x = -0.670683314Subproblem 2
x + 14.5 = -13.829316686 Simplifying x + 14.5 = -13.829316686 Reorder the terms: 14.5 + x = -13.829316686 Solving 14.5 + x = -13.829316686 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14.5' to each side of the equation. 14.5 + -14.5 + x = -13.829316686 + -14.5 Combine like terms: 14.5 + -14.5 = 0.0 0.0 + x = -13.829316686 + -14.5 x = -13.829316686 + -14.5 Combine like terms: -13.829316686 + -14.5 = -28.329316686 x = -28.329316686 Simplifying x = -28.329316686Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.670683314, -28.329316686}
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