5t^2+25t+10=0

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Solution for 5t^2+25t+10=0 equation: 


Simplifying
5t2 + 25t + 10 = 0

Reorder the terms:
10 + 25t + 5t2 = 0

Solving
10 + 25t + 5t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '5'.
5(2 + 5t + t2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(2 + 5t + t2)' equal to zero and attempt to solve:

Simplifying
2 + 5t + t2 = 0

Solving
2 + 5t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 5t + -2 + t2 = 0 + -2

Reorder the terms:
2 + -2 + 5t + t2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 5t + t2 = 0 + -2
5t + t2 = 0 + -2

Combine like terms: 0 + -2 = -2
5t + t2 = -2

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 = -2 + 6.25

Reorder the terms:
6.25 + 5t + t2 = -2 + 6.25

Combine like terms: -2 + 6.25 = 4.25
6.25 + 5t + t2 = 4.25

Factor a perfect square on the left side:
(t + 2.5)(t + 2.5) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(t + 2.5) equal to 2.061552813 and -2.061552813.


Subproblem 1
t + 2.5 = 2.061552813

Simplifying
t + 2.5 = 2.061552813

Reorder the terms:
2.5 + t = 2.061552813

Solving
2.5 + t = 2.061552813

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 = 2.061552813 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + t = 2.061552813 + -2.5
t = 2.061552813 + -2.5

Combine like terms: 2.061552813 + -2.5 = -0.438447187
t = -0.438447187

Simplifying
t = -0.438447187


Subproblem 2
t + 2.5 = -2.061552813

Simplifying
t + 2.5 = -2.061552813

Reorder the terms:
2.5 + t = -2.061552813

Solving
2.5 + t = -2.061552813

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 = -2.061552813 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + t = -2.061552813 + -2.5
t = -2.061552813 + -2.5

Combine like terms: -2.061552813 + -2.5 = -4.561552813
t = -4.561552813

Simplifying
t = -4.561552813


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-0.438447187, -4.561552813}
Solution
t = {-0.438447187, -4.561552813}

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