550=45x+x^2

Solution for 550=45x+x^2 equation:

Simplifying
550 = 45x + x2

Solving
550 = 45x + x2

Solving for variable 'x'.

Reorder the terms:
550 + -45x + -1x2 = 45x + -45x + x2 + -1x2

Combine like terms: 45x + -45x = 0
550 + -45x + -1x2 = 0 + x2 + -1x2
550 + -45x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
550 + -45x + -1x2 = 0

Factor a trinomial.
(10 + -1x)(55 + x) = 0

Subproblem 1
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Subproblem 2
Set the factor '(55 + x)' equal to zero and attempt to solve:

Simplifying
55 + x = 0

Solving
55 + x = 0

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

Add '-55' to each side of the equation.
55 + -55 + x = 0 + -55

Combine like terms: 55 + -55 = 0
0 + x = 0 + -55
x = 0 + -55

Combine like terms: 0 + -55 = -55
x = -55

Simplifying
x = -55
Solution
x = {10, -55}