0.9a^2+5.4a=4

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Solution for 0.9a^2+5.4a=4 equation:


Simplifying
0.9a2 + 5.4a = 4

Reorder the terms:
5.4a + 0.9a2 = 4

Solving
5.4a + 0.9a2 = 4

Solving for variable 'a'.

Reorder the terms:
-4 + 5.4a + 0.9a2 = 4 + -4

Combine like terms: 4 + -4 = 0
-4 + 5.4a + 0.9a2 = 0

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

Divide each side by '0.9'.
-4.444444444 + 6a + a2 = 0

Move the constant term to the right:

Add '4.444444444' to each side of the equation.
-4.444444444 + 6a + 4.444444444 + a2 = 0 + 4.444444444

Reorder the terms:
-4.444444444 + 4.444444444 + 6a + a2 = 0 + 4.444444444

Combine like terms: -4.444444444 + 4.444444444 = 0.000000000
0.000000000 + 6a + a2 = 0 + 4.444444444
6a + a2 = 0 + 4.444444444

Combine like terms: 0 + 4.444444444 = 4.444444444
6a + a2 = 4.444444444

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 = 4.444444444 + 9

Reorder the terms:
9 + 6a + a2 = 4.444444444 + 9

Combine like terms: 4.444444444 + 9 = 13.444444444
9 + 6a + a2 = 13.444444444

Factor a perfect square on the left side:
(a + 3)(a + 3) = 13.444444444

Calculate the square root of the right side: 3.666666667

Break this problem into two subproblems by setting 
(a + 3) equal to 3.666666667 and -3.666666667.

Subproblem 1

a + 3 = 3.666666667 Simplifying a + 3 = 3.666666667 Reorder the terms: 3 + a = 3.666666667 Solving 3 + a = 3.666666667 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 = 3.666666667 + -3 Combine like terms: 3 + -3 = 0 0 + a = 3.666666667 + -3 a = 3.666666667 + -3 Combine like terms: 3.666666667 + -3 = 0.666666667 a = 0.666666667 Simplifying a = 0.666666667

Subproblem 2

a + 3 = -3.666666667 Simplifying a + 3 = -3.666666667 Reorder the terms: 3 + a = -3.666666667 Solving 3 + a = -3.666666667 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 = -3.666666667 + -3 Combine like terms: 3 + -3 = 0 0 + a = -3.666666667 + -3 a = -3.666666667 + -3 Combine like terms: -3.666666667 + -3 = -6.666666667 a = -6.666666667 Simplifying a = -6.666666667

Solution

The solution to the problem is based on the solutions from the subproblems. a = {0.666666667, -6.666666667}

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