x² - 8x = 5
Solve for the roots by completing the square:
x² - 8x + (-8/2)² = 5 + (-8/2)²
x² - 8x + (-4)² = 5 + 16
(x - 4)² = 21
Solve by extracting the roots:
√(x-4)² = +/-√21
x - 4 = +/-√21
Solution:
Using the completing the square, we have
x² - 8x = 5
x² - 8x + (-4)² = 5 + (-4)²
x² - 8x + 16 = 5 + 16
Factor out x² - 8x + 16, then we obtain,
(x - 4)² = 21
By extracting the roots, we obtain,
√(x-4)² = ⁺₋√21
x - 4 = ⁺₋√21
x = 4 +√21
and
x = 4-√21
