x^2-sqrt(2)x-1=0

Solution for x^2-sqrt(2)x-1=0 equation:

Simplifying
x2 + -1sqrt(2) * x + -1 = 0

Reorder the terms for easier multiplication:
x2 + -1 * 2qrst * x + -1 = 0

Multiply -1 * 2
x2 + -2qrst * x + -1 = 0

Multiply qrst * x
x2 + -2qrstx + -1 = 0

Reorder the terms:
-1 + -2qrstx + x2 = 0

Solving
-1 + -2qrstx + x2 = 0

Solving for variable 'q'.

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

Add '1' to each side of the equation.
-1 + -2qrstx + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -2qrstx + x2 = 0 + 1

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

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

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

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

Divide each side by '-2rstx'.
q = -0.5r-1s-1t-1x-1 + 0.5r-1s-1t-1x

Simplifying
q = -0.5r-1s-1t-1x-1 + 0.5r-1s-1t-1x