4.2176=(0.45+x)*(5.325-x)

Solution for 4.2176=(0.45+x)*(5.325-x) equation:

Simplifying
4.2176 = (0.45 + x)(5.325 + -1x)

Multiply (0.45 + x) * (5.325 + -1x)
4.2176 = (0.45(5.325 + -1x) + x(5.325 + -1x))
4.2176 = ((5.325 * 0.45 + -1x * 0.45) + x(5.325 + -1x))
4.2176 = ((2.39625 + -0.45x) + x(5.325 + -1x))
4.2176 = (2.39625 + -0.45x + (5.325 * x + -1x * x))
4.2176 = (2.39625 + -0.45x + (5.325x + -1x2))

Combine like terms: -0.45x + 5.325x = 4.875x
4.2176 = (2.39625 + 4.875x + -1x2)

Solving
4.2176 = 2.39625 + 4.875x + -1x2

Solving for variable 'x'.

Combine like terms: 4.2176 + -2.39625 = 1.82135
1.82135 + -4.875x + x2 = 2.39625 + 4.875x + -1x2 + -2.39625 + -4.875x + x2

Reorder the terms:
1.82135 + -4.875x + x2 = 2.39625 + -2.39625 + 4.875x + -4.875x + -1x2 + x2

Combine like terms: 2.39625 + -2.39625 = 0.00000
1.82135 + -4.875x + x2 = 0.00000 + 4.875x + -4.875x + -1x2 + x2
1.82135 + -4.875x + x2 = 4.875x + -4.875x + -1x2 + x2

Combine like terms: 4.875x + -4.875x = 0.000
1.82135 + -4.875x + x2 = 0.000 + -1x2 + x2
1.82135 + -4.875x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
1.82135 + -4.875x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1.82135' to each side of the equation.
1.82135 + -4.875x + -1.82135 + x2 = 0 + -1.82135

Reorder the terms:
1.82135 + -1.82135 + -4.875x + x2 = 0 + -1.82135

Combine like terms: 1.82135 + -1.82135 = 0.00000
0.00000 + -4.875x + x2 = 0 + -1.82135
-4.875x + x2 = 0 + -1.82135

Combine like terms: 0 + -1.82135 = -1.82135
-4.875x + x2 = -1.82135

The x term is -4.875x.  Take half its coefficient (-2.4375).
Square it (5.94140625) and add it to both sides.

Add '5.94140625' to each side of the equation.
-4.875x + 5.94140625 + x2 = -1.82135 + 5.94140625

Reorder the terms:
5.94140625 + -4.875x + x2 = -1.82135 + 5.94140625

Combine like terms: -1.82135 + 5.94140625 = 4.12005625
5.94140625 + -4.875x + x2 = 4.12005625

Factor a perfect square on the left side:
(x + -2.4375)(x + -2.4375) = 4.12005625

Calculate the square root of the right side: 2.029792169

Break this problem into two subproblems by setting 
(x + -2.4375) equal to 2.029792169 and -2.029792169.

Subproblem 1
x + -2.4375 = 2.029792169

Simplifying
x + -2.4375 = 2.029792169

Reorder the terms:
-2.4375 + x = 2.029792169

Solving
-2.4375 + x = 2.029792169

Solving for variable 'x'.

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

Add '2.4375' to each side of the equation.
-2.4375 + 2.4375 + x = 2.029792169 + 2.4375

Combine like terms: -2.4375 + 2.4375 = 0.0000
0.0000 + x = 2.029792169 + 2.4375
x = 2.029792169 + 2.4375

Combine like terms: 2.029792169 + 2.4375 = 4.467292169
x = 4.467292169

Simplifying
x = 4.467292169

Subproblem 2
x + -2.4375 = -2.029792169

Simplifying
x + -2.4375 = -2.029792169

Reorder the terms:
-2.4375 + x = -2.029792169

Solving
-2.4375 + x = -2.029792169

Solving for variable 'x'.

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

Add '2.4375' to each side of the equation.
-2.4375 + 2.4375 + x = -2.029792169 + 2.4375

Combine like terms: -2.4375 + 2.4375 = 0.0000
0.0000 + x = -2.029792169 + 2.4375
x = -2.029792169 + 2.4375

Combine like terms: -2.029792169 + 2.4375 = 0.407707831
x = 0.407707831

Simplifying
x = 0.407707831

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.467292169, 0.407707831}