How do you solve t^2=6t+55?

t ² - 6 t - 55 = 0
( t - 11 ) ( t + 5 ) = 0
t = 11 , t = - 5

t² = 6t + 55
t² – 6t – 55 = 0
t² + 5t – 11t – 55 = 0
(t + 5) – 11(t + 5) = 0
(t + 5)(t – 11) = 0
(t + 5) = 0 or (t – 11) = 0
t = – 5 or t = 11

move everything to one side:

t^2 - 6t - 55 = 0

factor if possible. If not use the quadratic formula.

(t-11)(t+5) = 0

t = 11 or t = -5

Since this is a quadratic equation we can put this is in standard form... something equal 0...

t^2 -6t -55=0
Now factor

(t-11)(t+5)=0

Use the zero property

t-11=0 and t+5=0
t=11 and t=-5

t^2-6t-55=0

(t+5)(t-11)=0

t= -5 t=11

t^2 - 6t - 55 =0
which factorises to
(t-11)(t+5)=0
so t=11 and t=-5

t^2-6t-55=0
t^2-11t+5t-55=0
t(t-11)+5(t-11)=0
(t-11)(t+5)=0
t=11 or t=-5

make it into a quadratic:

t^2 - 6t - 55 = 0

(t+5)(t-11) = 0

t= -5 or t= 11

Use the quadratic formula:
t^2 - 6t - 55 = 0
t = (6 +- sqrt(6^2 + 4*55))/2
= (6 +- sqrt(256))/2
= (6 +- 16)/2
= 3 +- 8
= -5 and +11.

Or you could just see that the factorization is
(t-11)(t+5) = 0.

t^2 = 6t + 55
t^2 - 6t - 55 = 0
(t + 5)(t - 11) = 0

t + 5 = 0
t = -5

t - 11 = 0
t = 11

∴ t = -5 , 11