151=-5t(t-11)

Solution for 151=-5t(t-11) equation:

Simplifying
151 = -5t(t + -11)

Reorder the terms:
151 = -5t(-11 + t)
151 = (-11 * -5t + t * -5t)
151 = (55t + -5t2)

Solving
151 = 55t + -5t2

Solving for variable 't'.

Reorder the terms:
151 + -55t + 5t2 = 55t + -55t + -5t2 + 5t2

Combine like terms: 55t + -55t = 0
151 + -55t + 5t2 = 0 + -5t2 + 5t2
151 + -55t + 5t2 = -5t2 + 5t2

Combine like terms: -5t2 + 5t2 = 0
151 + -55t + 5t2 = 0

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
30.2 + -11t + t2 = 0

Move the constant term to the right:

Add '-30.2' to each side of the equation.
30.2 + -11t + -30.2 + t2 = 0 + -30.2

Reorder the terms:
30.2 + -30.2 + -11t + t2 = 0 + -30.2

Combine like terms: 30.2 + -30.2 = 0.0
0.0 + -11t + t2 = 0 + -30.2
-11t + t2 = 0 + -30.2

Combine like terms: 0 + -30.2 = -30.2
-11t + t2 = -30.2

The t term is -11t.  Take half its coefficient (-5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
-11t + 30.25 + t2 = -30.2 + 30.25

Reorder the terms:
30.25 + -11t + t2 = -30.2 + 30.25

Combine like terms: -30.2 + 30.25 = 0.05
30.25 + -11t + t2 = 0.05

Factor a perfect square on the left side:
(t + -5.5)(t + -5.5) = 0.05

Calculate the square root of the right side: 0.223606798

Break this problem into two subproblems by setting 
(t + -5.5) equal to 0.223606798 and -0.223606798.

Subproblem 1
t + -5.5 = 0.223606798

Simplifying
t + -5.5 = 0.223606798

Reorder the terms:
-5.5 + t = 0.223606798

Solving
-5.5 + t = 0.223606798

Solving for variable 't'.

Move all terms containing t to the left, all other terms to the right.

Add '5.5' to each side of the equation.
-5.5 + 5.5 + t = 0.223606798 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + t = 0.223606798 + 5.5
t = 0.223606798 + 5.5

Combine like terms: 0.223606798 + 5.5 = 5.723606798
t = 5.723606798

Simplifying
t = 5.723606798

Subproblem 2
t + -5.5 = -0.223606798

Simplifying
t + -5.5 = -0.223606798

Reorder the terms:
-5.5 + t = -0.223606798

Solving
-5.5 + t = -0.223606798

Solving for variable 't'.

Move all terms containing t to the left, all other terms to the right.

Add '5.5' to each side of the equation.
-5.5 + 5.5 + t = -0.223606798 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + t = -0.223606798 + 5.5
t = -0.223606798 + 5.5

Combine like terms: -0.223606798 + 5.5 = 5.276393202
t = 5.276393202

Simplifying
t = 5.276393202

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {5.723606798, 5.276393202}