Write x2 - 2x + 5 = 0 in vertex form. (Be sure to write your response in the form a (x-h) ^2+k=0 with no spaces!)

To write the given quadratic equation to its vertex form, we first form a perfect square.

x² - 2x + 5 = 0

Transpose the constant to other side of the equation,

x² - 2x = - 5

Complete the square in the left side of the equation,

x² - 2x + (-2/1 (2)) ² = - 5 + (-2/1 (2)) ²

Performed the operation,

x² - 2x + 1 = - 5 + 1

Factor the left side of the equation,

(x - 1) ² = - 4

Thus, the vertex form of the equation is,

(x-1) ² + 4 = 0