# Find the roots in three methods . x^2-x-6=0 completing the square/quadratic formula/factoring

2
by emelyly

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by emelyly

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(x-3)(x+2)=0

completing: (x^2+x+1/4)+6+1/4

√ x+1/2=√25/4

x+1/2=+-5/2

x=-1+5/2=4/2 or 2

x=-1-5/2=-6/2 or -3

COMPLETING THE SQUARE: ax² + bx + (b/2)² = c + (b/2)²

x² - x - 6 = 0

x² - x + (1/2)² = 6 + (1/2)²

x² - x + 1/4 = 6 + 1/4 (LCD is 4)

(x-1/2)² = (24+1)/4

x-1/2 = + or - 5/2

x = 5/2 + 1/2

x = 6/2

x = 3

x = -5/2 + 1/2

x = -4/2

x = -2

FACTORING:

x² - x -6 = 0

Factor: (x - 3) (x + 2) = 0

x-3 = 0

x = 3

x+ 2 = 0

x = -2

x = 3 ; x = -2