a(a+4)=71.69

Solution for a(a+4)=71.69 equation:

Simplifying
a(a + 4) = 71.69

Reorder the terms:
a(4 + a) = 71.69
(4 * a + a * a) = 71.69
(4a + a2) = 71.69

Solving
4a + a2 = 71.69

Solving for variable 'a'.

Reorder the terms:
-71.69 + 4a + a2 = 71.69 + -71.69

Combine like terms: 71.69 + -71.69 = 0.00
-71.69 + 4a + a2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '71.69' to each side of the equation.
-71.69 + 4a + 71.69 + a2 = 0.00 + 71.69

Reorder the terms:
-71.69 + 71.69 + 4a + a2 = 0.00 + 71.69

Combine like terms: -71.69 + 71.69 = 0.00
0.00 + 4a + a2 = 0.00 + 71.69
4a + a2 = 0.00 + 71.69

Combine like terms: 0.00 + 71.69 = 71.69
4a + a2 = 71.69

The a term is 4a.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4a + 4 + a2 = 71.69 + 4

Reorder the terms:
4 + 4a + a2 = 71.69 + 4

Combine like terms: 71.69 + 4 = 75.69
4 + 4a + a2 = 75.69

Factor a perfect square on the left side:
(a + 2)(a + 2) = 75.69

Calculate the square root of the right side: 8.7

Break this problem into two subproblems by setting 
(a + 2) equal to 8.7 and -8.7.

Subproblem 1
a + 2 = 8.7

Simplifying
a + 2 = 8.7

Reorder the terms:
2 + a = 8.7

Solving
2 + a = 8.7

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + a = 8.7 + -2

Combine like terms: 2 + -2 = 0
0 + a = 8.7 + -2
a = 8.7 + -2

Combine like terms: 8.7 + -2 = 6.7
a = 6.7

Simplifying
a = 6.7

Subproblem 2
a + 2 = -8.7

Simplifying
a + 2 = -8.7

Reorder the terms:
2 + a = -8.7

Solving
2 + a = -8.7

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + a = -8.7 + -2

Combine like terms: 2 + -2 = 0
0 + a = -8.7 + -2
a = -8.7 + -2

Combine like terms: -8.7 + -2 = -10.7
a = -10.7

Simplifying
a = -10.7

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {6.7, -10.7}