Solving Using the Quadratic Formula

Question

 

3t(t + 2) = 1

Answer 1

Expand: 3t^2 + 6t = 1

Put in quadratic form: 3t^2 + 6t -1 = 0

a=3, b=6, c=-1

Apply the formula: t = [-b ± sqrt (b² - 4ac)] / 2a

 

t = [-6 ± sqrt(36 +12)] / 6

 

Separate into 2 terms:          t = -1 ± sqrt (48) /6

 

Simplifying:   t = -1 ± 4√3 / 6

 

t = -1 ± (2√3) / 3

 

Answer 2

3t(t + 2) = 1

3t² + 6t - 1 = 0       a = 3, b = 6, c = -1

t = -b ±√(b² - 4ac)

             2a

t = -6 ±√[(6)² - 4(3)(-1)]

                 2(3)

 

t = -6 ±√[36 +12] 

                6

t = -6 ±√48

          6

t = -6 ±√16 √3

             6

t = -6 ± 4√3

           6

t = -3 ± 2√3

           3