Question

solve the following quadratic equation by completing square method first X square + X - 20 is equal to zero​

Answer 1

Solution :

⇒ x² + x - 20 = 0

⇒ x² + x = 20

⇒ x² + 2 × x × 1/2 = 20

⇒ x² + 2 × x × 1/2 + ( 1/2 )² = 20 + ( 1/2 )²

⇒ ( x + 1/2 )² = 20 + 1/4

⇒ ( x + 1/2 )² = ( 80 + 1 )/4

⇒ ( x + 1/2 )² = 81/4

⇒ x + 1/2 = ± √( 81/4 )

⇒ x + 1/2 = ± 9/2

⇒ x = -1/2 ± 9/2

⇒ x = ( -1/2 + 9/2 ) or x = ( -1/2 - 9/2 )

⇒ x = 8/2 or x = -10/2

⇒ x = 4 or x = -5

Answer 2

$\huge\sf\pink{Answer}$

☞ x = 4 or -5

$\rule{110}1$

$\huge\sf\blue{Given}$

✭ x²+x-20

$\rule{110}1$

$\huge\sf\gray{To \:Find}$

◈ Go solve by completing square method

$\rule{110}1$

$\huge\sf\purple{Steps}$

➝ $\sf x^2+x-20=0$

➝ $\sf x^2+x=20$

➝ $\sf x^2 \times x \times (\dfrac{1}{2})^2 = 20+\dfrac{1}{2}$

➝ $\sf (x+\dfrac{1}{2})^2 = \dfrac{80+1}{4}$

➝ $\sf (x+\dfrac{1}{2})^2 = \dfrac{81}{4}$

➝ $\sf (x+\dfrac{1}{2}) = \sqrt{\pm \dfrac{81}{4}}$

➝ $\sf (x+\dfrac{1}{2} = \pm \dfrac{9}{2}$

➝ $\sf x = -\dfrac{1}{2} \pm \dfrac{9}{2}$

➝ $\sf{ x = \dfrac{8}{2} \ or \ \dfrac{-10}{2}}$

➝ $\sf\orange{x = 4} \ or \ \red{-5}$

$\rule{170}3$