7=2+25t-5t^2

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Solution for 7=2+25t-5t^2 equation: 


Simplifying
7 = 2 + 25t + -5t2

Solving
7 = 2 + 25t + -5t2

Solving for variable 't'.

Combine like terms: 7 + -2 = 5
5 + -25t + 5t2 = 2 + 25t + -5t2 + -2 + -25t + 5t2

Reorder the terms:
5 + -25t + 5t2 = 2 + -2 + 25t + -25t + -5t2 + 5t2

Combine like terms: 2 + -2 = 0
5 + -25t + 5t2 = 0 + 25t + -25t + -5t2 + 5t2
5 + -25t + 5t2 = 25t + -25t + -5t2 + 5t2

Combine like terms: 25t + -25t = 0
5 + -25t + 5t2 = 0 + -5t2 + 5t2
5 + -25t + 5t2 = -5t2 + 5t2

Combine like terms: -5t2 + 5t2 = 0
5 + -25t + 5t2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(1 + -5t + t2) = 0

Ignore the factor 5.

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

Simplifying
1 + -5t + t2 = 0

Solving
1 + -5t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -5t + -1 + t2 = 0 + -1

Reorder the terms:
1 + -1 + -5t + t2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5t + t2 = 0 + -1
-5t + t2 = 0 + -1

Combine like terms: 0 + -1 = -1
-5t + t2 = -1

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 = -1 + 6.25

Reorder the terms:
6.25 + -5t + t2 = -1 + 6.25

Combine like terms: -1 + 6.25 = 5.25
6.25 + -5t + t2 = 5.25

Factor a perfect square on the left side:
(t + -2.5)(t + -2.5) = 5.25

Calculate the square root of the right side: 2.291287847

Break this problem into two subproblems by setting 
(t + -2.5) equal to 2.291287847 and -2.291287847.


Subproblem 1
t + -2.5 = 2.291287847

Simplifying
t + -2.5 = 2.291287847

Reorder the terms:
-2.5 + t = 2.291287847

Solving
-2.5 + t = 2.291287847

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 = 2.291287847 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + t = 2.291287847 + 2.5
t = 2.291287847 + 2.5

Combine like terms: 2.291287847 + 2.5 = 4.791287847
t = 4.791287847

Simplifying
t = 4.791287847


Subproblem 2
t + -2.5 = -2.291287847

Simplifying
t + -2.5 = -2.291287847

Reorder the terms:
-2.5 + t = -2.291287847

Solving
-2.5 + t = -2.291287847

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 = -2.291287847 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + t = -2.291287847 + 2.5
t = -2.291287847 + 2.5

Combine like terms: -2.291287847 + 2.5 = 0.208712153
t = 0.208712153

Simplifying
t = 0.208712153


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {4.791287847, 0.208712153}
Solution
t = {4.791287847, 0.208712153}

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