t^2-7t+8=0

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Solution for t^2-7t+8=0 equation: 


Simplifying
t2 + -7t + 8 = 0

Reorder the terms:
8 + -7t + t2 = 0

Solving
8 + -7t + t2 = 0

Solving for variable 't'.

Begin completing the square.

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + -7t + -8 + t2 = 0 + -8

Reorder the terms:
8 + -8 + -7t + t2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -7t + t2 = 0 + -8
-7t + t2 = 0 + -8

Combine like terms: 0 + -8 = -8
-7t + t2 = -8

The t term is -7t.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7t + 12.25 + t2 = -8 + 12.25

Reorder the terms:
12.25 + -7t + t2 = -8 + 12.25

Combine like terms: -8 + 12.25 = 4.25
12.25 + -7t + t2 = 4.25

Factor a perfect square on the left side:
(t + -3.5)(t + -3.5) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(t + -3.5) equal to 2.061552813 and -2.061552813.


Subproblem 1
t + -3.5 = 2.061552813

Simplifying
t + -3.5 = 2.061552813

Reorder the terms:
-3.5 + t = 2.061552813

Solving
-3.5 + t = 2.061552813

Solving for variable 't'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + t = 2.061552813 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + t = 2.061552813 + 3.5
t = 2.061552813 + 3.5

Combine like terms: 2.061552813 + 3.5 = 5.561552813
t = 5.561552813

Simplifying
t = 5.561552813


Subproblem 2
t + -3.5 = -2.061552813

Simplifying
t + -3.5 = -2.061552813

Reorder the terms:
-3.5 + t = -2.061552813

Solving
-3.5 + t = -2.061552813

Solving for variable 't'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + t = -2.061552813 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + t = -2.061552813 + 3.5
t = -2.061552813 + 3.5

Combine like terms: -2.061552813 + 3.5 = 1.438447187
t = 1.438447187

Simplifying
t = 1.438447187


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {5.561552813, 1.438447187}

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