Solve x2 - 8x + 5 = 0 using the completing-the-square method.

Solution:

Given x² - 8x + 5 = 0

x² - 8x = -5

Here a = 1, b = -8 and c = 5

We make a perfect square trinomial using completing the square method.

In order to make it a perfect square, we need to add (b/2)² on both sides: (-8/2)² = 16

x² - 8x +16 = -5 + 16

x² - 2(x)(4) + 4² = 11

We know that a² - 2ab + b² = (a - b)²

(x - 4)² = 11

x - 4 = ±√11

x = 4 + √11 or x = 4 - √11

Solve x² - 8x + 5 = 0 using the completing-the-square method.

Summary:

By solving x² - 8x + 5 = 0 using the completing-the-square method, we got x = 4 + √11 or x = 4 - √11