a^2+5a+2=0

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Solution for a^2+5a+2=0 equation:


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 = -0.438447187

Subproblem 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 = -4.561552813

Solution

The solution to the problem is based on the solutions from the subproblems. a = {-0.438447187, -4.561552813}

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