t^2+5t-8=0

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Solution for t^2+5t-8=0 equation: 


Simplifying
t2 + 5t + -8 = 0

Reorder the terms:
-8 + 5t + t2 = 0

Solving
-8 + 5t + 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 + 5t + 8 + t2 = 0 + 8

Reorder the terms:
-8 + 8 + 5t + t2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 5t + t2 = 0 + 8
5t + t2 = 0 + 8

Combine like terms: 0 + 8 = 8
5t + t2 = 8

The t term is 5t.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5t + 6.25 + t2 = 8 + 6.25

Reorder the terms:
6.25 + 5t + t2 = 8 + 6.25

Combine like terms: 8 + 6.25 = 14.25
6.25 + 5t + t2 = 14.25

Factor a perfect square on the left side:
(t + 2.5)(t + 2.5) = 14.25

Calculate the square root of the right side: 3.774917218

Break this problem into two subproblems by setting 
(t + 2.5) equal to 3.774917218 and -3.774917218.


Subproblem 1
t + 2.5 = 3.774917218

Simplifying
t + 2.5 = 3.774917218

Reorder the terms:
2.5 + t = 3.774917218

Solving
2.5 + t = 3.774917218

Solving for variable 't'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + t = 3.774917218 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + t = 3.774917218 + -2.5
t = 3.774917218 + -2.5

Combine like terms: 3.774917218 + -2.5 = 1.274917218
t = 1.274917218

Simplifying
t = 1.274917218


Subproblem 2
t + 2.5 = -3.774917218

Simplifying
t + 2.5 = -3.774917218

Reorder the terms:
2.5 + t = -3.774917218

Solving
2.5 + t = -3.774917218

Solving for variable 't'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + t = -3.774917218 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + t = -3.774917218 + -2.5
t = -3.774917218 + -2.5

Combine like terms: -3.774917218 + -2.5 = -6.274917218
t = -6.274917218

Simplifying
t = -6.274917218


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.274917218, -6.274917218}

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