x^2=50x-400

Solution for x^2=50x-400 equation:

Simplifying
x2 = 50x + -400

Reorder the terms:
x2 = -400 + 50x

Solving
x2 = -400 + 50x

Solving for variable 'x'.

Reorder the terms:
400 + -50x + x2 = -400 + 50x + 400 + -50x

Reorder the terms:
400 + -50x + x2 = -400 + 400 + 50x + -50x

Combine like terms: -400 + 400 = 0
400 + -50x + x2 = 0 + 50x + -50x
400 + -50x + x2 = 50x + -50x

Combine like terms: 50x + -50x = 0
400 + -50x + x2 = 0

Factor a trinomial.
(10 + -1x)(40 + -1x) = 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 '(40 + -1x)' equal to zero and attempt to solve:

Simplifying
40 + -1x = 0

Solving
40 + -1x = 0

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

Add '-40' to each side of the equation.
40 + -40 + -1x = 0 + -40

Combine like terms: 40 + -40 = 0
0 + -1x = 0 + -40
-1x = 0 + -40

Combine like terms: 0 + -40 = -40
-1x = -40

Divide each side by '-1'.
x = 40

Simplifying
x = 40
Solution
x = {10, 40}