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Simplifying x2 + 19x + 29 = 0 Reorder the terms: 29 + 19x + x2 = 0 Solving 29 + 19x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-29' to each side of the equation. 29 + 19x + -29 + x2 = 0 + -29 Reorder the terms: 29 + -29 + 19x + x2 = 0 + -29 Combine like terms: 29 + -29 = 0 0 + 19x + x2 = 0 + -29 19x + x2 = 0 + -29 Combine like terms: 0 + -29 = -29 19x + x2 = -29 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 = -29 + 90.25 Reorder the terms: 90.25 + 19x + x2 = -29 + 90.25 Combine like terms: -29 + 90.25 = 61.25 90.25 + 19x + x2 = 61.25 Factor a perfect square on the left side: (x + 9.5)(x + 9.5) = 61.25 Calculate the square root of the right side: 7.826237921 Break this problem into two subproblems by setting (x + 9.5) equal to 7.826237921 and -7.826237921.Subproblem 1
x + 9.5 = 7.826237921 Simplifying x + 9.5 = 7.826237921 Reorder the terms: 9.5 + x = 7.826237921 Solving 9.5 + x = 7.826237921 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 = 7.826237921 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = 7.826237921 + -9.5 x = 7.826237921 + -9.5 Combine like terms: 7.826237921 + -9.5 = -1.673762079 x = -1.673762079 Simplifying x = -1.673762079Subproblem 2
x + 9.5 = -7.826237921 Simplifying x + 9.5 = -7.826237921 Reorder the terms: 9.5 + x = -7.826237921 Solving 9.5 + x = -7.826237921 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 = -7.826237921 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = -7.826237921 + -9.5 x = -7.826237921 + -9.5 Combine like terms: -7.826237921 + -9.5 = -17.326237921 x = -17.326237921 Simplifying x = -17.326237921Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.673762079, -17.326237921}
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