Solve x² - 12x + 5 = 0 using the completing-the-square method.

Solution:

Given x² - 12x + 5 = 0

This is similar to quadratic equation ax² + bx + c = 0

Add (b/2)² on both sides

Here b = -12

Add (-12/2)² = (-6)² = 36

x² - 12x + 36 = -5 + 36

x² - 2(x)(6) + 6² = 31

This is in the form a² - 2ab + b² = (a - b)²

(x - 6)² = 31

x - 6 = ±√31

x = ±√31 + 6

Therefore, the solution is x = 6 ± √31

Solve x² - 12x + 5 = 0 using the completing-the-square method.

Summary:

Using the completing-the-square method for x² - 12x + 5 = 0, we get a solution as x = 6 ± √31.