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how to solve the x²-8x=5 in completing the square of quadratic equation?

Sagot :

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

x = 4 +√21  and  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