(x-14)(x-14)=400

Solution for (x-14)(x-14)=400 equation:

Simplifying
(x + -14)(x + -14) = 400

Reorder the terms:
(-14 + x)(x + -14) = 400

Reorder the terms:
(-14 + x)(-14 + x) = 400

Multiply (-14 + x) * (-14 + x)
(-14(-14 + x) + x(-14 + x)) = 400
((-14 * -14 + x * -14) + x(-14 + x)) = 400
((196 + -14x) + x(-14 + x)) = 400
(196 + -14x + (-14 * x + x * x)) = 400
(196 + -14x + (-14x + x2)) = 400

Combine like terms: -14x + -14x = -28x
(196 + -28x + x2) = 400

Solving
196 + -28x + x2 = 400

Solving for variable 'x'.

Reorder the terms:
196 + -400 + -28x + x2 = 400 + -400

Combine like terms: 196 + -400 = -204
-204 + -28x + x2 = 400 + -400

Combine like terms: 400 + -400 = 0
-204 + -28x + x2 = 0

Factor a trinomial.
(-6 + -1x)(34 + -1x) = 0

Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6
Subproblem 2
Set the factor '(34 + -1x)' equal to zero and attempt to solve:

Simplifying
34 + -1x = 0

Solving
34 + -1x = 0

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

Add '-34' to each side of the equation.
34 + -34 + -1x = 0 + -34

Combine like terms: 34 + -34 = 0
0 + -1x = 0 + -34
-1x = 0 + -34

Combine like terms: 0 + -34 = -34
-1x = -34

Divide each side by '-1'.
x = 34

Simplifying
x = 34
Solution
x = {-6, 34}