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

Sagot :

factoring: x^2-x-6=0
              (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
For quadratic formula, substitute the values of a = 1; b=-1 and c = 6 to quadratic formula, you can do it.

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
[tex] \sqrt{( x^{2} - 1/2) ^{2} } = \sqrt{ \frac{25}{4} } [/tex]
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