Question

c. by completing the square
X2+5x+6=0
X2+2x=8
2x2+2x=24​

Answer 1

Answer:

{- 3, - 2} ; {- 4, 2} ; {- 4, 3}

Step-by-step explanation:

1). a² ± 2ab + b² = (a ± b)²

2). a² - b² = (a - b)(a + b)

~~~~~~~~~~~~

x² + 5x + 6 = 0

(x² + 2× $\frac{5}{2}$x + $\frac{25}{4}$ ) - $\frac{25}{4}$ + 6 = 0

(x + $\frac{5}{2}$ )² - ( $\frac{1}{2}$ )² = 0

(x + $\frac{5}{2}$ - $\frac{1}{2}$ )(x + $\frac{5}{2}$ + $\frac{1}{2}$ ) = 0

(x +2)(x + 3) = 0 ⇒ $x_{1}$ = - 3 and $x_{2}$ = - 2

--------

x² + 2x = 8

x² + 2×1×(x) + 1 = 8 + 1

(x + 1)² - 3² = 0

(x + 1 - 3)(x + 1 + 3) = 0

(x - 2)(x + 4) = 0 ⇒ $x_{1}$ = - 4 and $x_{2}$ = 2

--------

2x² + 2x - 24 = 0 ⇔ x² + x - 12 = 0

NOW IS YOUR TURN!! Complete it by yourself, it's very good for your practice.