t(t-1)=7

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Solution for t(t-1)=7 equation:


Simplifying
t(t + -1) = 7

Reorder the terms:
t(-1 + t) = 7
(-1 * t + t * t) = 7
(-1t + t2) = 7

Solving
-1t + t2 = 7

Solving for variable 't'.

Reorder the terms:
-7 + -1t + t2 = 7 + -7

Combine like terms: 7 + -7 = 0
-7 + -1t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + -1t + 7 + t2 = 0 + 7

Reorder the terms:
-7 + 7 + -1t + t2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1t + t2 = 0 + 7
-1t + t2 = 0 + 7

Combine like terms: 0 + 7 = 7
-1t + t2 = 7

The t term is -1t.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1t + 0.25 + t2 = 7 + 0.25

Reorder the terms:
0.25 + -1t + t2 = 7 + 0.25

Combine like terms: 7 + 0.25 = 7.25
0.25 + -1t + t2 = 7.25

Factor a perfect square on the left side:
(t + -0.5)(t + -0.5) = 7.25

Calculate the square root of the right side: 2.692582404

Break this problem into two subproblems by setting 
(t + -0.5) equal to 2.692582404 and -2.692582404.


Subproblem 1
t + -0.5 = 2.692582404

Simplifying
t + -0.5 = 2.692582404

Reorder the terms:
-0.5 + t = 2.692582404

Solving
-0.5 + t = 2.692582404

Solving for variable 't'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + t = 2.692582404 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + t = 2.692582404 + 0.5
t = 2.692582404 + 0.5

Combine like terms: 2.692582404 + 0.5 = 3.192582404
t = 3.192582404

Simplifying
t = 3.192582404


Subproblem 2
t + -0.5 = -2.692582404

Simplifying
t + -0.5 = -2.692582404

Reorder the terms:
-0.5 + t = -2.692582404

Solving
-0.5 + t = -2.692582404

Solving for variable 't'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + t = -2.692582404 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + t = -2.692582404 + 0.5
t = -2.692582404 + 0.5

Combine like terms: -2.692582404 + 0.5 = -2.192582404
t = -2.192582404

Simplifying
t = -2.192582404


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.192582404, -2.192582404}

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