Question

X2+x-20 how to solve it by completing square method

Answer 1

Answer:

x = + 4 and - 5

Step-by-step explanation:

→ x² + x - 20 = 0

→ x² + x = 20

→ x² + 2(½)x = 20

→ x² + 2(½)x + (½)² = 20 + (½)²

→ (x + ½)² = 20 + ¼

→ (x + ½)² = 81/4

→ x + ½ = √(81/4)

→ x = ± 9/2 - 1/2

Case 1: When + 9/2 is considered

→ x = 9/2 - 1/2

→ x = + 4

Case 2: When - 9/2 is considered

→ x = - 9/2 - 1/2

→ x = - 5

Answer 2

Solution :-

Given quadratic equation is

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