4a^2+11a+5=0

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Solution for 4a^2+11a+5=0 equation:


Simplifying
4a2 + 11a + 5 = 0

Reorder the terms:
5 + 11a + 4a2 = 0

Solving
5 + 11a + 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 + 2.75a + a2 = 0

Move the constant term to the right:

Add '-1.25' to each side of the equation.
1.25 + 2.75a + -1.25 + a2 = 0 + -1.25

Reorder the terms:
1.25 + -1.25 + 2.75a + a2 = 0 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + 2.75a + a2 = 0 + -1.25
2.75a + a2 = 0 + -1.25

Combine like terms: 0 + -1.25 = -1.25
2.75a + a2 = -1.25

The a term is 2.75a.  Take half its coefficient (1.375).
Square it (1.890625) and add it to both sides.

Add '1.890625' to each side of the equation.
2.75a + 1.890625 + a2 = -1.25 + 1.890625

Reorder the terms:
1.890625 + 2.75a + a2 = -1.25 + 1.890625

Combine like terms: -1.25 + 1.890625 = 0.640625
1.890625 + 2.75a + a2 = 0.640625

Factor a perfect square on the left side:
(a + 1.375)(a + 1.375) = 0.640625

Calculate the square root of the right side: 0.80039053

Break this problem into two subproblems by setting 
(a + 1.375) equal to 0.80039053 and -0.80039053.

Subproblem 1

a + 1.375 = 0.80039053 Simplifying a + 1.375 = 0.80039053 Reorder the terms: 1.375 + a = 0.80039053 Solving 1.375 + a = 0.80039053 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1.375' to each side of the equation. 1.375 + -1.375 + a = 0.80039053 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + a = 0.80039053 + -1.375 a = 0.80039053 + -1.375 Combine like terms: 0.80039053 + -1.375 = -0.57460947 a = -0.57460947 Simplifying a = -0.57460947

Subproblem 2

a + 1.375 = -0.80039053 Simplifying a + 1.375 = -0.80039053 Reorder the terms: 1.375 + a = -0.80039053 Solving 1.375 + a = -0.80039053 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1.375' to each side of the equation. 1.375 + -1.375 + a = -0.80039053 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + a = -0.80039053 + -1.375 a = -0.80039053 + -1.375 Combine like terms: -0.80039053 + -1.375 = -2.17539053 a = -2.17539053 Simplifying a = -2.17539053

Solution

The solution to the problem is based on the solutions from the subproblems. a = {-0.57460947, -2.17539053}

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