Question

Solve the following quadratic equations by factorization method.

Answer 1

${(2x + 3)}^{2} - 81 \\ {(2x)}^{2} + {3}^{2} + 2 \times 2x \times 3 - 81 \\ 4 {x}^{2} + 9 + 12x - 81 \\ 4 {x}^{2} + 12x - 72 \\ 4 {x}^{2} - 12x + 24x - 72 \\ 4x(x - 3) + 24( x - 3) \\ (4x + 24)(x - 3)$
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Answer 2

Given

( 2x + 3 )² - 81 = 0

=> ( 2x + 3 )² - 9² = 0

=>(2x+3+9)( 2x+3-9)=0

[By algebraic identity

a² - b² = ( a + b )( a - b )]

=> ( 2x + 12)( 2x - 6 ) = 0

=> 2x+12 = 0 or 2x-6=0

=> 2x = -12 or 2x = 6

=> x = -12/2 or x = 6/2

x = -6 or x = 3

Therefore ,

x = -6 or x = 3

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