0=a^2-6a-100

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Solution for 0=a^2-6a-100 equation:


Simplifying
0 = a2 + -6a + -100

Reorder the terms:
0 = -100 + -6a + a2

Solving
0 = -100 + -6a + a2

Solving for variable 'a'.

Combine like terms: 0 + 100 = 100
100 + 6a + -1a2 = -100 + -6a + a2 + 100 + 6a + -1a2

Reorder the terms:
100 + 6a + -1a2 = -100 + 100 + -6a + 6a + a2 + -1a2

Combine like terms: -100 + 100 = 0
100 + 6a + -1a2 = 0 + -6a + 6a + a2 + -1a2
100 + 6a + -1a2 = -6a + 6a + a2 + -1a2

Combine like terms: -6a + 6a = 0
100 + 6a + -1a2 = 0 + a2 + -1a2
100 + 6a + -1a2 = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
100 + 6a + -1a2 = 0

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

Divide each side by '-1'.
-100 + -6a + a2 = 0

Move the constant term to the right:

Add '100' to each side of the equation.
-100 + -6a + 100 + a2 = 0 + 100

Reorder the terms:
-100 + 100 + -6a + a2 = 0 + 100

Combine like terms: -100 + 100 = 0
0 + -6a + a2 = 0 + 100
-6a + a2 = 0 + 100

Combine like terms: 0 + 100 = 100
-6a + a2 = 100

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 = 100 + 9

Reorder the terms:
9 + -6a + a2 = 100 + 9

Combine like terms: 100 + 9 = 109
9 + -6a + a2 = 109

Factor a perfect square on the left side:
(a + -3)(a + -3) = 109

Calculate the square root of the right side: 10.440306509

Break this problem into two subproblems by setting 
(a + -3) equal to 10.440306509 and -10.440306509.

Subproblem 1

a + -3 = 10.440306509 Simplifying a + -3 = 10.440306509 Reorder the terms: -3 + a = 10.440306509 Solving -3 + a = 10.440306509 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 = 10.440306509 + 3 Combine like terms: -3 + 3 = 0 0 + a = 10.440306509 + 3 a = 10.440306509 + 3 Combine like terms: 10.440306509 + 3 = 13.440306509 a = 13.440306509 Simplifying a = 13.440306509

Subproblem 2

a + -3 = -10.440306509 Simplifying a + -3 = -10.440306509 Reorder the terms: -3 + a = -10.440306509 Solving -3 + a = -10.440306509 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 = -10.440306509 + 3 Combine like terms: -3 + 3 = 0 0 + a = -10.440306509 + 3 a = -10.440306509 + 3 Combine like terms: -10.440306509 + 3 = -7.440306509 a = -7.440306509 Simplifying a = -7.440306509

Solution

The solution to the problem is based on the solutions from the subproblems. a = {13.440306509, -7.440306509}

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