4+10a+a^2-3(a-2)-13=

Solution for 4+10a+a^2-3(a-2)-13= equation:

Simplifying
4 + 10a + a2 + -3(a + -2) + -13 = 0

Reorder the terms:
4 + 10a + a2 + -3(-2 + a) + -13 = 0
4 + 10a + a2 + (-2 * -3 + a * -3) + -13 = 0
4 + 10a + a2 + (6 + -3a) + -13 = 0

Reorder the terms:
4 + 6 + -13 + 10a + -3a + a2 = 0

Combine like terms: 4 + 6 = 10
10 + -13 + 10a + -3a + a2 = 0

Combine like terms: 10 + -13 = -3
-3 + 10a + -3a + a2 = 0

Combine like terms: 10a + -3a = 7a
-3 + 7a + a2 = 0

Solving
-3 + 7a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 7a + 3 + a2 = 0 + 3

Reorder the terms:
-3 + 3 + 7a + a2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 7a + a2 = 0 + 3
7a + a2 = 0 + 3

Combine like terms: 0 + 3 = 3
7a + a2 = 3

The a term is 7a.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7a + 12.25 + a2 = 3 + 12.25

Reorder the terms:
12.25 + 7a + a2 = 3 + 12.25

Combine like terms: 3 + 12.25 = 15.25
12.25 + 7a + a2 = 15.25

Factor a perfect square on the left side:
(a + 3.5)(a + 3.5) = 15.25

Calculate the square root of the right side: 3.905124838

Break this problem into two subproblems by setting 
(a + 3.5) equal to 3.905124838 and -3.905124838.

Subproblem 1
a + 3.5 = 3.905124838

Simplifying
a + 3.5 = 3.905124838

Reorder the terms:
3.5 + a = 3.905124838

Solving
3.5 + a = 3.905124838

Solving for variable 'a'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + a = 3.905124838 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + a = 3.905124838 + -3.5
a = 3.905124838 + -3.5

Combine like terms: 3.905124838 + -3.5 = 0.405124838
a = 0.405124838

Simplifying
a = 0.405124838

Subproblem 2
a + 3.5 = -3.905124838

Simplifying
a + 3.5 = -3.905124838

Reorder the terms:
3.5 + a = -3.905124838

Solving
3.5 + a = -3.905124838

Solving for variable 'a'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + a = -3.905124838 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + a = -3.905124838 + -3.5
a = -3.905124838 + -3.5

Combine like terms: -3.905124838 + -3.5 = -7.405124838
a = -7.405124838

Simplifying
a = -7.405124838

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {0.405124838, -7.405124838}