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Simplifying x2 + 5x + 1 = 0 Reorder the terms: 1 + 5x + x2 = 0 Solving 1 + 5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + 5x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 5x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 5x + x2 = 0 + -1 5x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 5x + x2 = -1 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 = -1 + 6.25 Reorder the terms: 6.25 + 5x + x2 = -1 + 6.25 Combine like terms: -1 + 6.25 = 5.25 6.25 + 5x + x2 = 5.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (x + 2.5) equal to 2.291287847 and -2.291287847.Subproblem 1
x + 2.5 = 2.291287847 Simplifying x + 2.5 = 2.291287847 Reorder the terms: 2.5 + x = 2.291287847 Solving 2.5 + x = 2.291287847 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 = 2.291287847 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 2.291287847 + -2.5 x = 2.291287847 + -2.5 Combine like terms: 2.291287847 + -2.5 = -0.208712153 x = -0.208712153 Simplifying x = -0.208712153Subproblem 2
x + 2.5 = -2.291287847 Simplifying x + 2.5 = -2.291287847 Reorder the terms: 2.5 + x = -2.291287847 Solving 2.5 + x = -2.291287847 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 = -2.291287847 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -2.291287847 + -2.5 x = -2.291287847 + -2.5 Combine like terms: -2.291287847 + -2.5 = -4.791287847 x = -4.791287847 Simplifying x = -4.791287847Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.208712153, -4.791287847}
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