Use Quadratic Formula to Factor

Factor using the quadratic formula.

-sqrt{2}(x^2) + x = -sqrt{2}

(√2)x^2 - x - √2 = 0

x = (1 ± √(1^2 - 4*√2*-√2))/(2√2)
x = (1 ± √(1 + 4√2^2))/(2√2)
x = (1 ± √(1 + 4*2))/(2√2)
x = (1 ± √9)/(2√2)
x = (1 ± 3)/(2√2)
x = √2(1 ± 3)/(2√2^2)
x = (√2 ± 3√2)/(2*2)
x = (√2 ± 3√2)/4

x = (√2 + 3√2)/4 = (4√2)/4 = √2

x = (√2 - 3√2)/4 = (-2√2)/4 = -√2/2

(x - (√2))(x - (-√2/2))

(x - √2)(x + √2/2)

-√2 x² + x = -√2
(-√2 x + 1)x = -√2

But I bet you really wanted it factored after gathering everything into the LHS:
-√2 x² + x + √2 = 0 which can also be written
2x² - √2 x - 2 = 0

(a,b,c) = (2, -√2, -2)

∆ = b² - 4ac = 2 + 16 = 18
x = (-b ± √∆)/2a = (√2 ± 3√2)/4 = {4, -2} / 2√2 = {√2, -1/√2}

2x² - √2 x - 2 = 2(x - √2)(x + 1/√2) = (x - √2)(2x + √2)
or if you want it the way it was before re-writing,

-√2 x² + x + √2 = -(x - √2)(√2 x + 1)