a*(a+10)-6=104

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Solution for a*(a+10)-6=104 equation:


Simplifying
a(a + 10) + -6 = 104

Reorder the terms:
a(10 + a) + -6 = 104
(10 * a + a * a) + -6 = 104
(10a + a2) + -6 = 104

Reorder the terms:
-6 + 10a + a2 = 104

Solving
-6 + 10a + a2 = 104

Solving for variable 'a'.

Reorder the terms:
-6 + -104 + 10a + a2 = 104 + -104

Combine like terms: -6 + -104 = -110
-110 + 10a + a2 = 104 + -104

Combine like terms: 104 + -104 = 0
-110 + 10a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '110' to each side of the equation.
-110 + 10a + 110 + a2 = 0 + 110

Reorder the terms:
-110 + 110 + 10a + a2 = 0 + 110

Combine like terms: -110 + 110 = 0
0 + 10a + a2 = 0 + 110
10a + a2 = 0 + 110

Combine like terms: 0 + 110 = 110
10a + a2 = 110

The a term is 10a.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10a + 25 + a2 = 110 + 25

Reorder the terms:
25 + 10a + a2 = 110 + 25

Combine like terms: 110 + 25 = 135
25 + 10a + a2 = 135

Factor a perfect square on the left side:
(a + 5)(a + 5) = 135

Calculate the square root of the right side: 11.618950039

Break this problem into two subproblems by setting 
(a + 5) equal to 11.618950039 and -11.618950039.

Subproblem 1

a + 5 = 11.618950039 Simplifying a + 5 = 11.618950039 Reorder the terms: 5 + a = 11.618950039 Solving 5 + a = 11.618950039 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + a = 11.618950039 + -5 Combine like terms: 5 + -5 = 0 0 + a = 11.618950039 + -5 a = 11.618950039 + -5 Combine like terms: 11.618950039 + -5 = 6.618950039 a = 6.618950039 Simplifying a = 6.618950039

Subproblem 2

a + 5 = -11.618950039 Simplifying a + 5 = -11.618950039 Reorder the terms: 5 + a = -11.618950039 Solving 5 + a = -11.618950039 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + a = -11.618950039 + -5 Combine like terms: 5 + -5 = 0 0 + a = -11.618950039 + -5 a = -11.618950039 + -5 Combine like terms: -11.618950039 + -5 = -16.618950039 a = -16.618950039 Simplifying a = -16.618950039

Solution

The solution to the problem is based on the solutions from the subproblems. a = {6.618950039, -16.618950039}

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