How do I solve this?

Question

t(2t+9)=-7

Answer 1

How do I solve this?
t(2t+9)=-7

t(2t + 9) = -7
2t^2 + 9t = -7
t^2 + 4.5t = -3.5
Add the square of half the co-efficient of t.
t^2 + 4.5t + 2.25^2 = -3.5 + 2.25^2
(t + 2.25)^2 = 1.5625
t + 2.25 = ±√1.5625
t + 2.25 = ± 1.25
t = 1.25 - 2.25     and  t = -1.25 - 2.25
t = -1              and t = -3.5

Check

t(2t + 9) = -7
-1(2(-1) + 9) = -7
-(-2 + 9) = -7
-(7) = -7
-7 = -7

t(2t + 9) = -7
-3.5(2(-3.5) + 9) = -7
-3.5(-7 + 9) = -7
-3.5(2) = -7
-7 = -7

It checks: t = -1 and t = -3.5