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