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Simplifying a2 + 5a + 2 = 0 Reorder the terms: 2 + 5a + a2 = 0 Solving 2 + 5a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + 5a + -2 + a2 = 0 + -2 Reorder the terms: 2 + -2 + 5a + a2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 5a + a2 = 0 + -2 5a + a2 = 0 + -2 Combine like terms: 0 + -2 = -2 5a + a2 = -2 The a term is 5a. 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. 5a + 6.25 + a2 = -2 + 6.25 Reorder the terms: 6.25 + 5a + a2 = -2 + 6.25 Combine like terms: -2 + 6.25 = 4.25 6.25 + 5a + a2 = 4.25 Factor a perfect square on the left side: (a + 2.5)(a + 2.5) = 4.25 Calculate the square root of the right side: 2.061552813 Break this problem into two subproblems by setting (a + 2.5) equal to 2.061552813 and -2.061552813.Subproblem 1
a + 2.5 = 2.061552813 Simplifying a + 2.5 = 2.061552813 Reorder the terms: 2.5 + a = 2.061552813 Solving 2.5 + a = 2.061552813 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + a = 2.061552813 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + a = 2.061552813 + -2.5 a = 2.061552813 + -2.5 Combine like terms: 2.061552813 + -2.5 = -0.438447187 a = -0.438447187 Simplifying a = -0.438447187Subproblem 2
a + 2.5 = -2.061552813 Simplifying a + 2.5 = -2.061552813 Reorder the terms: 2.5 + a = -2.061552813 Solving 2.5 + a = -2.061552813 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + a = -2.061552813 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + a = -2.061552813 + -2.5 a = -2.061552813 + -2.5 Combine like terms: -2.061552813 + -2.5 = -4.561552813 a = -4.561552813 Simplifying a = -4.561552813Solution
The solution to the problem is based on the solutions from the subproblems. a = {-0.438447187, -4.561552813}
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