(3-x)(3-x)+x^2=5

Solution for (3-x)(3-x)+x^2=5 equation:

Simplifying
(3 + -1x)(3 + -1x) + x2 = 5

Multiply (3 + -1x) * (3 + -1x)
(3(3 + -1x) + -1x * (3 + -1x)) + x2 = 5
((3 * 3 + -1x * 3) + -1x * (3 + -1x)) + x2 = 5
((9 + -3x) + -1x * (3 + -1x)) + x2 = 5
(9 + -3x + (3 * -1x + -1x * -1x)) + x2 = 5
(9 + -3x + (-3x + 1x2)) + x2 = 5

Combine like terms: -3x + -3x = -6x
(9 + -6x + 1x2) + x2 = 5

Combine like terms: 1x2 + x2 = 2x2
9 + -6x + 2x2 = 5

Solving
9 + -6x + 2x2 = 5

Solving for variable 'x'.

Reorder the terms:
9 + -5 + -6x + 2x2 = 5 + -5

Combine like terms: 9 + -5 = 4
4 + -6x + 2x2 = 5 + -5

Combine like terms: 5 + -5 = 0
4 + -6x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + -3x + x2) = 0

Factor a trinomial.
2((1 + -1x)(2 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1

Combine like terms: 0 + -1 = -1
-1x = -1

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {1, 2}