230=a^2+3a

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Solution for 230=a^2+3a equation:


Simplifying
230 = a2 + 3a

Reorder the terms:
230 = 3a + a2

Solving
230 = 3a + a2

Solving for variable 'a'.

Reorder the terms:
230 + -3a + -1a2 = 3a + -3a + a2 + -1a2

Combine like terms: 3a + -3a = 0
230 + -3a + -1a2 = 0 + a2 + -1a2
230 + -3a + -1a2 = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
230 + -3a + -1a2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-230 + 3a + a2 = 0

Move the constant term to the right:

Add '230' to each side of the equation.
-230 + 3a + 230 + a2 = 0 + 230

Reorder the terms:
-230 + 230 + 3a + a2 = 0 + 230

Combine like terms: -230 + 230 = 0
0 + 3a + a2 = 0 + 230
3a + a2 = 0 + 230

Combine like terms: 0 + 230 = 230
3a + a2 = 230

The a term is 3a.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3a + 2.25 + a2 = 230 + 2.25

Reorder the terms:
2.25 + 3a + a2 = 230 + 2.25

Combine like terms: 230 + 2.25 = 232.25
2.25 + 3a + a2 = 232.25

Factor a perfect square on the left side:
(a + 1.5)(a + 1.5) = 232.25

Calculate the square root of the right side: 15.239750654

Break this problem into two subproblems by setting 
(a + 1.5) equal to 15.239750654 and -15.239750654.

Subproblem 1

a + 1.5 = 15.239750654 Simplifying a + 1.5 = 15.239750654 Reorder the terms: 1.5 + a = 15.239750654 Solving 1.5 + a = 15.239750654 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + a = 15.239750654 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + a = 15.239750654 + -1.5 a = 15.239750654 + -1.5 Combine like terms: 15.239750654 + -1.5 = 13.739750654 a = 13.739750654 Simplifying a = 13.739750654

Subproblem 2

a + 1.5 = -15.239750654 Simplifying a + 1.5 = -15.239750654 Reorder the terms: 1.5 + a = -15.239750654 Solving 1.5 + a = -15.239750654 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + a = -15.239750654 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + a = -15.239750654 + -1.5 a = -15.239750654 + -1.5 Combine like terms: -15.239750654 + -1.5 = -16.739750654 a = -16.739750654 Simplifying a = -16.739750654

Solution

The solution to the problem is based on the solutions from the subproblems. a = {13.739750654, -16.739750654}

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