25a^2-40a+16=45

Solution for 25a^2-40a+16=45 equation:

Simplifying
25a2 + -40a + 16 = 45

Reorder the terms:
16 + -40a + 25a2 = 45

Solving
16 + -40a + 25a2 = 45

Solving for variable 'a'.

Reorder the terms:
16 + -45 + -40a + 25a2 = 45 + -45

Combine like terms: 16 + -45 = -29
-29 + -40a + 25a2 = 45 + -45

Combine like terms: 45 + -45 = 0
-29 + -40a + 25a2 = 0

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

Divide each side by '25'.
-1.16 + -1.6a + a2 = 0

Move the constant term to the right:

Add '1.16' to each side of the equation.
-1.16 + -1.6a + 1.16 + a2 = 0 + 1.16

Reorder the terms:
-1.16 + 1.16 + -1.6a + a2 = 0 + 1.16

Combine like terms: -1.16 + 1.16 = 0.00
0.00 + -1.6a + a2 = 0 + 1.16
-1.6a + a2 = 0 + 1.16

Combine like terms: 0 + 1.16 = 1.16
-1.6a + a2 = 1.16

The a term is -1.6a.  Take half its coefficient (-0.8).
Square it (0.64) and add it to both sides.

Add '0.64' to each side of the equation.
-1.6a + 0.64 + a2 = 1.16 + 0.64

Reorder the terms:
0.64 + -1.6a + a2 = 1.16 + 0.64

Combine like terms: 1.16 + 0.64 = 1.8
0.64 + -1.6a + a2 = 1.8

Factor a perfect square on the left side:
(a + -0.8)(a + -0.8) = 1.8

Calculate the square root of the right side: 1.341640787

Break this problem into two subproblems by setting 
(a + -0.8) equal to 1.341640787 and -1.341640787.

Subproblem 1
a + -0.8 = 1.341640787

Simplifying
a + -0.8 = 1.341640787

Reorder the terms:
-0.8 + a = 1.341640787

Solving
-0.8 + a = 1.341640787

Solving for variable 'a'.

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

Add '0.8' to each side of the equation.
-0.8 + 0.8 + a = 1.341640787 + 0.8

Combine like terms: -0.8 + 0.8 = 0.0
0.0 + a = 1.341640787 + 0.8
a = 1.341640787 + 0.8

Combine like terms: 1.341640787 + 0.8 = 2.141640787
a = 2.141640787

Simplifying
a = 2.141640787

Subproblem 2
a + -0.8 = -1.341640787

Simplifying
a + -0.8 = -1.341640787

Reorder the terms:
-0.8 + a = -1.341640787

Solving
-0.8 + a = -1.341640787

Solving for variable 'a'.

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

Add '0.8' to each side of the equation.
-0.8 + 0.8 + a = -1.341640787 + 0.8

Combine like terms: -0.8 + 0.8 = 0.0
0.0 + a = -1.341640787 + 0.8
a = -1.341640787 + 0.8

Combine like terms: -1.341640787 + 0.8 = -0.541640787
a = -0.541640787

Simplifying
a = -0.541640787

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {2.141640787, -0.541640787}