3a(5+9a)+(4a-12)=

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Solution for 3a(5+9a)+(4a-12)= equation:


Simplifying
3a(5 + 9a) + (4a + -12) = 0
(5 * 3a + 9a * 3a) + (4a + -12) = 0
(15a + 27a2) + (4a + -12) = 0

Reorder the terms:
15a + 27a2 + (-12 + 4a) = 0

Remove parenthesis around (-12 + 4a)
15a + 27a2 + -12 + 4a = 0

Reorder the terms:
-12 + 15a + 4a + 27a2 = 0

Combine like terms: 15a + 4a = 19a
-12 + 19a + 27a2 = 0

Solving
-12 + 19a + 27a2 = 0

Solving for variable 'a'.

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

Divide each side by '27'.
-0.4444444444 + 0.7037037037a + a2 = 0

Move the constant term to the right:

Add '0.4444444444' to each side of the equation.
-0.4444444444 + 0.7037037037a + 0.4444444444 + a2 = 0 + 0.4444444444

Reorder the terms:
-0.4444444444 + 0.4444444444 + 0.7037037037a + a2 = 0 + 0.4444444444

Combine like terms: -0.4444444444 + 0.4444444444 = 0.0000000000
0.0000000000 + 0.7037037037a + a2 = 0 + 0.4444444444
0.7037037037a + a2 = 0 + 0.4444444444

Combine like terms: 0 + 0.4444444444 = 0.4444444444
0.7037037037a + a2 = 0.4444444444

The a term is 0.7037037037a.  Take half its coefficient (0.3518518519).
Square it (0.1237997257) and add it to both sides.

Add '0.1237997257' to each side of the equation.
0.7037037037a + 0.1237997257 + a2 = 0.4444444444 + 0.1237997257

Reorder the terms:
0.1237997257 + 0.7037037037a + a2 = 0.4444444444 + 0.1237997257

Combine like terms: 0.4444444444 + 0.1237997257 = 0.5682441701
0.1237997257 + 0.7037037037a + a2 = 0.5682441701

Factor a perfect square on the left side:
(a + 0.3518518519)(a + 0.3518518519) = 0.5682441701

Calculate the square root of the right side: 0.75381972

Break this problem into two subproblems by setting 
(a + 0.3518518519) equal to 0.75381972 and -0.75381972.

Subproblem 1

a + 0.3518518519 = 0.75381972 Simplifying a + 0.3518518519 = 0.75381972 Reorder the terms: 0.3518518519 + a = 0.75381972 Solving 0.3518518519 + a = 0.75381972 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.3518518519' to each side of the equation. 0.3518518519 + -0.3518518519 + a = 0.75381972 + -0.3518518519 Combine like terms: 0.3518518519 + -0.3518518519 = 0.0000000000 0.0000000000 + a = 0.75381972 + -0.3518518519 a = 0.75381972 + -0.3518518519 Combine like terms: 0.75381972 + -0.3518518519 = 0.4019678681 a = 0.4019678681 Simplifying a = 0.4019678681

Subproblem 2

a + 0.3518518519 = -0.75381972 Simplifying a + 0.3518518519 = -0.75381972 Reorder the terms: 0.3518518519 + a = -0.75381972 Solving 0.3518518519 + a = -0.75381972 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.3518518519' to each side of the equation. 0.3518518519 + -0.3518518519 + a = -0.75381972 + -0.3518518519 Combine like terms: 0.3518518519 + -0.3518518519 = 0.0000000000 0.0000000000 + a = -0.75381972 + -0.3518518519 a = -0.75381972 + -0.3518518519 Combine like terms: -0.75381972 + -0.3518518519 = -1.1056715719 a = -1.1056715719 Simplifying a = -1.1056715719

Solution

The solution to the problem is based on the solutions from the subproblems. a = {0.4019678681, -1.1056715719}

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