0=a^2-6a-38

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Solution for 0=a^2-6a-38 equation:


Simplifying
0 = a2 + -6a + -38

Reorder the terms:
0 = -38 + -6a + a2

Solving
0 = -38 + -6a + a2

Solving for variable 'a'.

Combine like terms: 0 + 38 = 38
38 + 6a + -1a2 = -38 + -6a + a2 + 38 + 6a + -1a2

Reorder the terms:
38 + 6a + -1a2 = -38 + 38 + -6a + 6a + a2 + -1a2

Combine like terms: -38 + 38 = 0
38 + 6a + -1a2 = 0 + -6a + 6a + a2 + -1a2
38 + 6a + -1a2 = -6a + 6a + a2 + -1a2

Combine like terms: -6a + 6a = 0
38 + 6a + -1a2 = 0 + a2 + -1a2
38 + 6a + -1a2 = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
38 + 6a + -1a2 = 0

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

Divide each side by '-1'.
-38 + -6a + a2 = 0

Move the constant term to the right:

Add '38' to each side of the equation.
-38 + -6a + 38 + a2 = 0 + 38

Reorder the terms:
-38 + 38 + -6a + a2 = 0 + 38

Combine like terms: -38 + 38 = 0
0 + -6a + a2 = 0 + 38
-6a + a2 = 0 + 38

Combine like terms: 0 + 38 = 38
-6a + a2 = 38

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 = 38 + 9

Reorder the terms:
9 + -6a + a2 = 38 + 9

Combine like terms: 38 + 9 = 47
9 + -6a + a2 = 47

Factor a perfect square on the left side:
(a + -3)(a + -3) = 47

Calculate the square root of the right side: 6.8556546

Break this problem into two subproblems by setting 
(a + -3) equal to 6.8556546 and -6.8556546.

Subproblem 1

a + -3 = 6.8556546 Simplifying a + -3 = 6.8556546 Reorder the terms: -3 + a = 6.8556546 Solving -3 + a = 6.8556546 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 = 6.8556546 + 3 Combine like terms: -3 + 3 = 0 0 + a = 6.8556546 + 3 a = 6.8556546 + 3 Combine like terms: 6.8556546 + 3 = 9.8556546 a = 9.8556546 Simplifying a = 9.8556546

Subproblem 2

a + -3 = -6.8556546 Simplifying a + -3 = -6.8556546 Reorder the terms: -3 + a = -6.8556546 Solving -3 + a = -6.8556546 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 = -6.8556546 + 3 Combine like terms: -3 + 3 = 0 0 + a = -6.8556546 + 3 a = -6.8556546 + 3 Combine like terms: -6.8556546 + 3 = -3.8556546 a = -3.8556546 Simplifying a = -3.8556546

Solution

The solution to the problem is based on the solutions from the subproblems. a = {9.8556546, -3.8556546}

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