4a^2+40a+5=0

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Solution for 4a^2+40a+5=0 equation:


Simplifying
4a2 + 40a + 5 = 0

Reorder the terms:
5 + 40a + 4a2 = 0

Solving
5 + 40a + 4a2 = 0

Solving for variable 'a'.

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

Divide each side by '4'.
1.25 + 10a + a2 = 0

Move the constant term to the right:

Add '-1.25' to each side of the equation.
1.25 + 10a + -1.25 + a2 = 0 + -1.25

Reorder the terms:
1.25 + -1.25 + 10a + a2 = 0 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + 10a + a2 = 0 + -1.25
10a + a2 = 0 + -1.25

Combine like terms: 0 + -1.25 = -1.25
10a + a2 = -1.25

The a term is 10a.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10a + 25 + a2 = -1.25 + 25

Reorder the terms:
25 + 10a + a2 = -1.25 + 25

Combine like terms: -1.25 + 25 = 23.75
25 + 10a + a2 = 23.75

Factor a perfect square on the left side:
(a + 5)(a + 5) = 23.75

Calculate the square root of the right side: 4.873397172

Break this problem into two subproblems by setting 
(a + 5) equal to 4.873397172 and -4.873397172.

Subproblem 1

a + 5 = 4.873397172 Simplifying a + 5 = 4.873397172 Reorder the terms: 5 + a = 4.873397172 Solving 5 + a = 4.873397172 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + a = 4.873397172 + -5 Combine like terms: 5 + -5 = 0 0 + a = 4.873397172 + -5 a = 4.873397172 + -5 Combine like terms: 4.873397172 + -5 = -0.126602828 a = -0.126602828 Simplifying a = -0.126602828

Subproblem 2

a + 5 = -4.873397172 Simplifying a + 5 = -4.873397172 Reorder the terms: 5 + a = -4.873397172 Solving 5 + a = -4.873397172 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + a = -4.873397172 + -5 Combine like terms: 5 + -5 = 0 0 + a = -4.873397172 + -5 a = -4.873397172 + -5 Combine like terms: -4.873397172 + -5 = -9.873397172 a = -9.873397172 Simplifying a = -9.873397172

Solution

The solution to the problem is based on the solutions from the subproblems. a = {-0.126602828, -9.873397172}

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