X^3+37=X^3+2X^2+1

Solution for X^3+37=X^3+2X^2+1 equation:

Simplifying
X3 + 37 = X3 + 2X2 + 1

Reorder the terms:
37 + X3 = X3 + 2X2 + 1

Reorder the terms:
37 + X3 = 1 + 2X2 + X3

Add '-1X3' to each side of the equation.
37 + X3 + -1X3 = 1 + 2X2 + X3 + -1X3

Combine like terms: X3 + -1X3 = 0
37 + 0 = 1 + 2X2 + X3 + -1X3
37 = 1 + 2X2 + X3 + -1X3

Combine like terms: X3 + -1X3 = 0
37 = 1 + 2X2 + 0
37 = 1 + 2X2

Solving
37 = 1 + 2X2

Solving for variable 'X'.

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

Add '-2X2' to each side of the equation.
37 + -2X2 = 1 + 2X2 + -2X2

Combine like terms: 2X2 + -2X2 = 0
37 + -2X2 = 1 + 0
37 + -2X2 = 1

Add '-37' to each side of the equation.
37 + -37 + -2X2 = 1 + -37

Combine like terms: 37 + -37 = 0
0 + -2X2 = 1 + -37
-2X2 = 1 + -37

Combine like terms: 1 + -37 = -36
-2X2 = -36

Divide each side by '-2'.
X2 = 18

Simplifying
X2 = 18

Take the square root of each side:
X = {-4.242640687, 4.242640687}