0.2a^2+1.2a+0.9=0

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Solution for 0.2a^2+1.2a+0.9=0 equation:


Simplifying
0.2a2 + 1.2a + 0.9 = 0

Reorder the terms:
0.9 + 1.2a + 0.2a2 = 0

Solving
0.9 + 1.2a + 0.2a2 = 0

Solving for variable 'a'.

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

Divide each side by '0.2'.
4.5 + 6a + a2 = 0

Move the constant term to the right:

Add '-4.5' to each side of the equation.
4.5 + 6a + -4.5 + a2 = 0 + -4.5

Reorder the terms:
4.5 + -4.5 + 6a + a2 = 0 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + 6a + a2 = 0 + -4.5
6a + a2 = 0 + -4.5

Combine like terms: 0 + -4.5 = -4.5
6a + a2 = -4.5

The a term is 6a.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6a + 9 + a2 = -4.5 + 9

Reorder the terms:
9 + 6a + a2 = -4.5 + 9

Combine like terms: -4.5 + 9 = 4.5
9 + 6a + a2 = 4.5

Factor a perfect square on the left side:
(a + 3)(a + 3) = 4.5

Calculate the square root of the right side: 2.121320344

Break this problem into two subproblems by setting 
(a + 3) equal to 2.121320344 and -2.121320344.

Subproblem 1

a + 3 = 2.121320344 Simplifying a + 3 = 2.121320344 Reorder the terms: 3 + a = 2.121320344 Solving 3 + a = 2.121320344 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + a = 2.121320344 + -3 Combine like terms: 3 + -3 = 0 0 + a = 2.121320344 + -3 a = 2.121320344 + -3 Combine like terms: 2.121320344 + -3 = -0.878679656 a = -0.878679656 Simplifying a = -0.878679656

Subproblem 2

a + 3 = -2.121320344 Simplifying a + 3 = -2.121320344 Reorder the terms: 3 + a = -2.121320344 Solving 3 + a = -2.121320344 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + a = -2.121320344 + -3 Combine like terms: 3 + -3 = 0 0 + a = -2.121320344 + -3 a = -2.121320344 + -3 Combine like terms: -2.121320344 + -3 = -5.121320344 a = -5.121320344 Simplifying a = -5.121320344

Solution

The solution to the problem is based on the solutions from the subproblems. a = {-0.878679656, -5.121320344}

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