Question

Solve this equation:
$14 + b = \frac{240}{b}$
​

Answer 1

Answer:

Two possibilities:  b = -24 or b = 10

Step-by-step explanation:

14 + b = 240 / b

=> b ( 14 + b ) = 240

=> b² + 14b = 240     ... (1)

Solve by completing the square...

=> b² + 2×7b + 7² = 240 + 7²

=> ( b + 7 )² = 240 + 49 = 289

=> b + 7 = ± 17

=> b = -7 ± 17

=> b = -24 or b = 10

Solve by using the quadratic formula

From equation (1),

b² + 14b - 240 = 0

=> b = ( -14 ± √( 14² + 4×240 ) ) / 2

      = ( -14 ± √( 196 + 960 ) ) / 2

      = ( -14 ± √1156 ) / 2

      = ( -14 ± 34 ) / 2

      = ( -14 - 34 ) / 2    or    ( -14 + 34 ) / 2

      = -48 / 2    or    20 / 2

      = -24    or    10