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Simplifying x2 + 5x + -22 = 0 Reorder the terms: -22 + 5x + x2 = 0 Solving -22 + 5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '22' to each side of the equation. -22 + 5x + 22 + x2 = 0 + 22 Reorder the terms: -22 + 22 + 5x + x2 = 0 + 22 Combine like terms: -22 + 22 = 0 0 + 5x + x2 = 0 + 22 5x + x2 = 0 + 22 Combine like terms: 0 + 22 = 22 5x + x2 = 22 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 22 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 22 + 6.25 Combine like terms: 22 + 6.25 = 28.25 6.25 + 5x + x2 = 28.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 28.25 Calculate the square root of the right side: 5.315072906 Break this problem into two subproblems by setting (x + 2.5) equal to 5.315072906 and -5.315072906.Subproblem 1
x + 2.5 = 5.315072906 Simplifying x + 2.5 = 5.315072906 Reorder the terms: 2.5 + x = 5.315072906 Solving 2.5 + x = 5.315072906 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 5.315072906 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 5.315072906 + -2.5 x = 5.315072906 + -2.5 Combine like terms: 5.315072906 + -2.5 = 2.815072906 x = 2.815072906 Simplifying x = 2.815072906Subproblem 2
x + 2.5 = -5.315072906 Simplifying x + 2.5 = -5.315072906 Reorder the terms: 2.5 + x = -5.315072906 Solving 2.5 + x = -5.315072906 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -5.315072906 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -5.315072906 + -2.5 x = -5.315072906 + -2.5 Combine like terms: -5.315072906 + -2.5 = -7.815072906 x = -7.815072906 Simplifying x = -7.815072906Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.815072906, -7.815072906}
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