Question

(x+2)(x+3)=240,Find the roots of the given equation by the method of perfect square.

Answer 1

Hi ,

( x + 2 )( x + 3 ) = 240

x² + ( 2 + 3 )x + 2 × 3 = 240

x² + 5x + 6 = 240

x² + 5x = 240 - 6

x² + 5x = 234

x² + 2 × x × 5/2 = 234

x² + 2 × x × 2 + ( 5/2 )² = 234 + ( 5/2 )²

( x + 5/2 )² = 234 + 25/4

( x + 5/2 )² = ( 936 + 25 )/4

( x + 5/2 )² = 961/4

( x + 5/2 )² = ( 31/2 )²

x + 5/2 = ± 31/2

x = -5/2 ± 31/2

x = -5/2 + 31/2 or x = -5/2 - 31/2

x = 26/2 or x = -36/2

x = 13 or x = - 18

I hope this helps you.

: )

Answer 2

GIVEN :

(x+2)(x+3)=240

Standard form of quadratic equation : ax²+bx+c = 0

(x+2)(x+3)=240

x² + 3x + 2x + 6 = 240

x² + 5x - 240 + 6 = 0

Standard form of quadratic equation (x+2)(x+3)=240 is x² +5x - 234 = 0

To make it a perfect square We have to find the Third term

Third term = (Middle term)² / 4 × First term

Third term = (5x)²/ 4 × x² = 25x²/4x² = 25/4

Third term = 25/4

x² +5x + 25/4 - 25/4 - 234 = 0

[Adding & Subtracting Third term ]

(x + 5/2)² - (25/4 + 234) = 0

(x + 5/2)² - (25+936/4) = 0

(x + 5/2)² - 961/4 = 0

(x + 5/2)² - (31/2)² = 0

(x + 5/2 +31/2) (x + 5/2 - 31/2) = 0

(x + 36/2) (x - 26/2) = 0

(x +18) (x -13) = 0

(x +18) = 0 or (x -13) = 0

x = -18 or x = 13

Hence, the roots of the equation - 18 & 13.

HOPE THIS ANSWER WILL HELP YOU..