(8.2*8.2)=(4.2*4.2)+x*x

Solution for (8.2*8.2)=(4.2*4.2)+x*x equation:

Simplifying
(8.2 * 8.2) = (4.2 * 4.2) + x * x

Multiply 8.2 * 8.2
(67.24) = (4.2 * 4.2) + x * x
67.24 = (4.2 * 4.2) + x * x

Multiply 4.2 * 4.2
67.24 = (17.64) + x * x
67.24 = 17.64 + x * x

Multiply x * x
67.24 = 17.64 + x2

Solving
67.24 = 17.64 + x2

Solving for variable 'x'.

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

Add '-1x2' to each side of the equation.
67.24 + -1x2 = 17.64 + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
67.24 + -1x2 = 17.64 + 0
67.24 + -1x2 = 17.64

Add '-67.24' to each side of the equation.
67.24 + -67.24 + -1x2 = 17.64 + -67.24

Combine like terms: 67.24 + -67.24 = 0.00
0.00 + -1x2 = 17.64 + -67.24
-1x2 = 17.64 + -67.24

Combine like terms: 17.64 + -67.24 = -49.6
-1x2 = -49.6

Divide each side by '-1'.
x2 = 49.6

Simplifying
x2 = 49.6

Take the square root of each side:
x = {-7.042726745, 7.042726745}