27=w(w+w)+1

Solution for 27=w(w+w)+1 equation:

Simplifying
27 = w(w + w) + 1

Combine like terms: w + w = 2w
27 = w(2w) + 1

Remove parenthesis around (2w)
27 = w * 2w + 1

Reorder the terms for easier multiplication:
27 = 2w * w + 1

Multiply w * w
27 = 2w2 + 1

Reorder the terms:
27 = 1 + 2w2

Solving
27 = 1 + 2w2

Solving for variable 'w'.

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

Add '-2w2' to each side of the equation.
27 + -2w2 = 1 + 2w2 + -2w2

Combine like terms: 2w2 + -2w2 = 0
27 + -2w2 = 1 + 0
27 + -2w2 = 1

Add '-27' to each side of the equation.
27 + -27 + -2w2 = 1 + -27

Combine like terms: 27 + -27 = 0
0 + -2w2 = 1 + -27
-2w2 = 1 + -27

Combine like terms: 1 + -27 = -26
-2w2 = -26

Divide each side by '-2'.
w2 = 13

Simplifying
w2 = 13

Take the square root of each side:
w = {-3.605551275, 3.605551275}