5a^2+2a=27

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Solution for 5a^2+2a=27 equation:


Simplifying
5a2 + 2a = 27

Reorder the terms:
2a + 5a2 = 27

Solving
2a + 5a2 = 27

Solving for variable 'a'.

Reorder the terms:
-27 + 2a + 5a2 = 27 + -27

Combine like terms: 27 + -27 = 0
-27 + 2a + 5a2 = 0

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

Divide each side by '5'.
-5.4 + 0.4a + a2 = 0

Move the constant term to the right:

Add '5.4' to each side of the equation.
-5.4 + 0.4a + 5.4 + a2 = 0 + 5.4

Reorder the terms:
-5.4 + 5.4 + 0.4a + a2 = 0 + 5.4

Combine like terms: -5.4 + 5.4 = 0.0
0.0 + 0.4a + a2 = 0 + 5.4
0.4a + a2 = 0 + 5.4

Combine like terms: 0 + 5.4 = 5.4
0.4a + a2 = 5.4

The a term is 0.4a.  Take half its coefficient (0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
0.4a + 0.04 + a2 = 5.4 + 0.04

Reorder the terms:
0.04 + 0.4a + a2 = 5.4 + 0.04

Combine like terms: 5.4 + 0.04 = 5.44
0.04 + 0.4a + a2 = 5.44

Factor a perfect square on the left side:
(a + 0.2)(a + 0.2) = 5.44

Calculate the square root of the right side: 2.332380758

Break this problem into two subproblems by setting 
(a + 0.2) equal to 2.332380758 and -2.332380758.

Subproblem 1

a + 0.2 = 2.332380758 Simplifying a + 0.2 = 2.332380758 Reorder the terms: 0.2 + a = 2.332380758 Solving 0.2 + a = 2.332380758 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + a = 2.332380758 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + a = 2.332380758 + -0.2 a = 2.332380758 + -0.2 Combine like terms: 2.332380758 + -0.2 = 2.132380758 a = 2.132380758 Simplifying a = 2.132380758

Subproblem 2

a + 0.2 = -2.332380758 Simplifying a + 0.2 = -2.332380758 Reorder the terms: 0.2 + a = -2.332380758 Solving 0.2 + a = -2.332380758 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + a = -2.332380758 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + a = -2.332380758 + -0.2 a = -2.332380758 + -0.2 Combine like terms: -2.332380758 + -0.2 = -2.532380758 a = -2.532380758 Simplifying a = -2.532380758

Solution

The solution to the problem is based on the solutions from the subproblems. a = {2.132380758, -2.532380758}

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