Question

solve by factorization method 6(2x+1)²=(2x+1)+5​

Answer 1

ANSWER :–

x = 0 or x = -(11/12)

EXPLANATION :–

GIVEN :–

▪︎A quadratic equation – 6(2x+1)² = (2x+1) + 5

TO FIND :–

Value of 'x'.

SOLUTION :–

• Let's put (2x + 1) = t –

=> 6t² = t + 5

=> 6t² - t - 5 = 0

=> 6t² - 6t + 5t - 5 = 0

=> 6t(t - 1) + 5(t - 1) = 0

=> (6t + 5)(t - 1) = 0

=> t = -⅚ , t = 1

▪︎ Now put the value of 't' –

☞ When t = -⅚ –

=> (2x + 1) = - ⅚

=> 12x + 6 = -5

=> 12x = -11

=> x = -(11/12)

☞ When t = 1 –

=> 2x + 1 = 1

=> x = 0

Hence , x = 0 or x = -(11/12)

➪ VERIFICATION :–

☞ At x = 0 –

=> 6(2×0 + 1)² = (2×0 + 1) + 5

=> 6(1)² = 1 + 5

=> 6 = 6 (verified)

☞ At x = -(11/12) –

=> 6[2×(-11/12) + 1]² = [2×(-11/12) + 1] + 5

=> 6[1 - (11/6)]² = [1 - (11/6)] + 5

=> 6(-⅚)² = -⅚ + 5

=> (25/6) = (25/6) (verified)