5a^2+20a+3=0

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Solution for 5a^2+20a+3=0 equation:


Simplifying
5a2 + 20a + 3 = 0

Reorder the terms:
3 + 20a + 5a2 = 0

Solving
3 + 20a + 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'.
0.6 + 4a + a2 = 0

Move the constant term to the right:

Add '-0.6' to each side of the equation.
0.6 + 4a + -0.6 + a2 = 0 + -0.6

Reorder the terms:
0.6 + -0.6 + 4a + a2 = 0 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + 4a + a2 = 0 + -0.6
4a + a2 = 0 + -0.6

Combine like terms: 0 + -0.6 = -0.6
4a + a2 = -0.6

The a term is 4a.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4a + 4 + a2 = -0.6 + 4

Reorder the terms:
4 + 4a + a2 = -0.6 + 4

Combine like terms: -0.6 + 4 = 3.4
4 + 4a + a2 = 3.4

Factor a perfect square on the left side:
(a + 2)(a + 2) = 3.4

Calculate the square root of the right side: 1.843908891

Break this problem into two subproblems by setting 
(a + 2) equal to 1.843908891 and -1.843908891.

Subproblem 1

a + 2 = 1.843908891 Simplifying a + 2 = 1.843908891 Reorder the terms: 2 + a = 1.843908891 Solving 2 + a = 1.843908891 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + a = 1.843908891 + -2 Combine like terms: 2 + -2 = 0 0 + a = 1.843908891 + -2 a = 1.843908891 + -2 Combine like terms: 1.843908891 + -2 = -0.156091109 a = -0.156091109 Simplifying a = -0.156091109

Subproblem 2

a + 2 = -1.843908891 Simplifying a + 2 = -1.843908891 Reorder the terms: 2 + a = -1.843908891 Solving 2 + a = -1.843908891 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + a = -1.843908891 + -2 Combine like terms: 2 + -2 = 0 0 + a = -1.843908891 + -2 a = -1.843908891 + -2 Combine like terms: -1.843908891 + -2 = -3.843908891 a = -3.843908891 Simplifying a = -3.843908891

Solution

The solution to the problem is based on the solutions from the subproblems. a = {-0.156091109, -3.843908891}

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