How to solve : 16=2t + 0.25 t''squar

The solutions of the equation are t = 4 (√5 + 1) or 4 (√5 - 1).

Step-by-step explanation:

We have to solve the given quadratic equation of single variable t.

The equation is 16 = 2t + 0.25t²

⇒ 0.25t² + 2t - 16 = 0

⇒ 25t² + 200t - 1600 = 0 {Multiplying both sides with 100}

⇒ 25t² + 200t + 400 - 400 - 1600 = 0

⇒ (5t + 20) ² - 2000 = 0

⇒ (5t + 20) ² - (20√5) ² = 0

⇒ (5t + 20 + 20√5) (5t + 20 - 20√5) = 0

So, (5t + 20 + 20√5) = 0 or, (5t + 20 - 20√5) = 0

⇒ (t + 4 + 4√5) = 0 or, (t + 4 - 4√5) = 0

⇒ t = - 4 (1 + √5) or, t = 4 (√5 - 1) (Answer)