t^2-3t+2.25=4.25

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Solution for t^2-3t+2.25=4.25 equation: 


Simplifying
t2 + -3t + 2.25 = 4.25

Reorder the terms:
2.25 + -3t + t2 = 4.25

Solving
2.25 + -3t + t2 = 4.25

Solving for variable 't'.

Reorder the terms:
2.25 + -4.25 + -3t + t2 = 4.25 + -4.25

Combine like terms: 2.25 + -4.25 = -2
-2 + -3t + t2 = 4.25 + -4.25

Combine like terms: 4.25 + -4.25 = 0.00
-2 + -3t + t2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -3t + 2 + t2 = 0.00 + 2

Reorder the terms:
-2 + 2 + -3t + t2 = 0.00 + 2

Combine like terms: -2 + 2 = 0
0 + -3t + t2 = 0.00 + 2
-3t + t2 = 0.00 + 2

Combine like terms: 0.00 + 2 = 2
-3t + t2 = 2

The t term is -3t.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3t + 2.25 + t2 = 2 + 2.25

Reorder the terms:
2.25 + -3t + t2 = 2 + 2.25

Combine like terms: 2 + 2.25 = 4.25
2.25 + -3t + t2 = 4.25

Factor a perfect square on the left side:
(t + -1.5)(t + -1.5) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(t + -1.5) equal to 2.061552813 and -2.061552813.


Subproblem 1
t + -1.5 = 2.061552813

Simplifying
t + -1.5 = 2.061552813

Reorder the terms:
-1.5 + t = 2.061552813

Solving
-1.5 + t = 2.061552813

Solving for variable 't'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + t = 2.061552813 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + t = 2.061552813 + 1.5
t = 2.061552813 + 1.5

Combine like terms: 2.061552813 + 1.5 = 3.561552813
t = 3.561552813

Simplifying
t = 3.561552813


Subproblem 2
t + -1.5 = -2.061552813

Simplifying
t + -1.5 = -2.061552813

Reorder the terms:
-1.5 + t = -2.061552813

Solving
-1.5 + t = -2.061552813

Solving for variable 't'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + t = -2.061552813 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + t = -2.061552813 + 1.5
t = -2.061552813 + 1.5

Combine like terms: -2.061552813 + 1.5 = -0.561552813
t = -0.561552813

Simplifying
t = -0.561552813


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.561552813, -0.561552813}

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