5a^2+29a+10=0

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Solution for 5a^2+29a+10=0 equation:


Simplifying
5a2 + 29a + 10 = 0

Reorder the terms:
10 + 29a + 5a2 = 0

Solving
10 + 29a + 5a2 = 0

Solving for variable 'a'.

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
2 + 5.8a + a2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 5.8a + -2 + a2 = 0 + -2

Reorder the terms:
2 + -2 + 5.8a + a2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 5.8a + a2 = 0 + -2
5.8a + a2 = 0 + -2

Combine like terms: 0 + -2 = -2
5.8a + a2 = -2

The a term is 5.8a.  Take half its coefficient (2.9).
Square it (8.41) and add it to both sides.

Add '8.41' to each side of the equation.
5.8a + 8.41 + a2 = -2 + 8.41

Reorder the terms:
8.41 + 5.8a + a2 = -2 + 8.41

Combine like terms: -2 + 8.41 = 6.41
8.41 + 5.8a + a2 = 6.41

Factor a perfect square on the left side:
(a + 2.9)(a + 2.9) = 6.41

Calculate the square root of the right side: 2.53179778

Break this problem into two subproblems by setting 
(a + 2.9) equal to 2.53179778 and -2.53179778.

Subproblem 1

a + 2.9 = 2.53179778 Simplifying a + 2.9 = 2.53179778 Reorder the terms: 2.9 + a = 2.53179778 Solving 2.9 + a = 2.53179778 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2.9' to each side of the equation. 2.9 + -2.9 + a = 2.53179778 + -2.9 Combine like terms: 2.9 + -2.9 = 0.0 0.0 + a = 2.53179778 + -2.9 a = 2.53179778 + -2.9 Combine like terms: 2.53179778 + -2.9 = -0.36820222 a = -0.36820222 Simplifying a = -0.36820222

Subproblem 2

a + 2.9 = -2.53179778 Simplifying a + 2.9 = -2.53179778 Reorder the terms: 2.9 + a = -2.53179778 Solving 2.9 + a = -2.53179778 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2.9' to each side of the equation. 2.9 + -2.9 + a = -2.53179778 + -2.9 Combine like terms: 2.9 + -2.9 = 0.0 0.0 + a = -2.53179778 + -2.9 a = -2.53179778 + -2.9 Combine like terms: -2.53179778 + -2.9 = -5.43179778 a = -5.43179778 Simplifying a = -5.43179778

Solution

The solution to the problem is based on the solutions from the subproblems. a = {-0.36820222, -5.43179778}

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