a^2-3a=37+3a

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Solution for a^2-3a=37+3a equation:


Simplifying
a2 + -3a = 37 + 3a

Reorder the terms:
-3a + a2 = 37 + 3a

Solving
-3a + a2 = 37 + 3a

Solving for variable 'a'.

Reorder the terms:
-37 + -3a + -3a + a2 = 37 + 3a + -37 + -3a

Combine like terms: -3a + -3a = -6a
-37 + -6a + a2 = 37 + 3a + -37 + -3a

Reorder the terms:
-37 + -6a + a2 = 37 + -37 + 3a + -3a

Combine like terms: 37 + -37 = 0
-37 + -6a + a2 = 0 + 3a + -3a
-37 + -6a + a2 = 3a + -3a

Combine like terms: 3a + -3a = 0
-37 + -6a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '37' to each side of the equation.
-37 + -6a + 37 + a2 = 0 + 37

Reorder the terms:
-37 + 37 + -6a + a2 = 0 + 37

Combine like terms: -37 + 37 = 0
0 + -6a + a2 = 0 + 37
-6a + a2 = 0 + 37

Combine like terms: 0 + 37 = 37
-6a + a2 = 37

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 = 37 + 9

Reorder the terms:
9 + -6a + a2 = 37 + 9

Combine like terms: 37 + 9 = 46
9 + -6a + a2 = 46

Factor a perfect square on the left side:
(a + -3)(a + -3) = 46

Calculate the square root of the right side: 6.782329983

Break this problem into two subproblems by setting 
(a + -3) equal to 6.782329983 and -6.782329983.

Subproblem 1

a + -3 = 6.782329983 Simplifying a + -3 = 6.782329983 Reorder the terms: -3 + a = 6.782329983 Solving -3 + a = 6.782329983 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 = 6.782329983 + 3 Combine like terms: -3 + 3 = 0 0 + a = 6.782329983 + 3 a = 6.782329983 + 3 Combine like terms: 6.782329983 + 3 = 9.782329983 a = 9.782329983 Simplifying a = 9.782329983

Subproblem 2

a + -3 = -6.782329983 Simplifying a + -3 = -6.782329983 Reorder the terms: -3 + a = -6.782329983 Solving -3 + a = -6.782329983 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 = -6.782329983 + 3 Combine like terms: -3 + 3 = 0 0 + a = -6.782329983 + 3 a = -6.782329983 + 3 Combine like terms: -6.782329983 + 3 = -3.782329983 a = -3.782329983 Simplifying a = -3.782329983

Solution

The solution to the problem is based on the solutions from the subproblems. a = {9.782329983, -3.782329983}

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