31=2x^2-1

Solution for 31=2x^2-1 equation:

Simplifying
31 = 2x2 + -1

Reorder the terms:
31 = -1 + 2x2

Solving
31 = -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.
31 + -2x2 = -1 + 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
31 + -2x2 = -1 + 0
31 + -2x2 = -1

Add '-31' to each side of the equation.
31 + -31 + -2x2 = -1 + -31

Combine like terms: 31 + -31 = 0
0 + -2x2 = -1 + -31
-2x2 = -1 + -31

Combine like terms: -1 + -31 = -32
-2x2 = -32

Divide each side by '-2'.
x2 = 16

Simplifying
x2 = 16

Take the square root of each side:
x = {-4, 4}