2t(t-3)=10

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Solution for 2t(t-3)=10 equation:


Simplifying
2t(t + -3) = 10

Reorder the terms:
2t(-3 + t) = 10
(-3 * 2t + t * 2t) = 10
(-6t + 2t2) = 10

Solving
-6t + 2t2 = 10

Solving for variable 't'.

Reorder the terms:
-10 + -6t + 2t2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + -6t + 2t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + -3t + t2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-5 + -3t + t2)' equal to zero and attempt to solve:

Simplifying
-5 + -3t + t2 = 0

Solving
-5 + -3t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + -3t + 5 + t2 = 0 + 5

Reorder the terms:
-5 + 5 + -3t + t2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -3t + t2 = 0 + 5
-3t + t2 = 0 + 5

Combine like terms: 0 + 5 = 5
-3t + t2 = 5

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 = 5 + 2.25

Reorder the terms:
2.25 + -3t + t2 = 5 + 2.25

Combine like terms: 5 + 2.25 = 7.25
2.25 + -3t + t2 = 7.25

Factor a perfect square on the left side:
(t + -1.5)(t + -1.5) = 7.25

Calculate the square root of the right side: 2.692582404

Break this problem into two subproblems by setting 
(t + -1.5) equal to 2.692582404 and -2.692582404.


Subproblem 1
t + -1.5 = 2.692582404

Simplifying
t + -1.5 = 2.692582404

Reorder the terms:
-1.5 + t = 2.692582404

Solving
-1.5 + t = 2.692582404

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 = 2.692582404 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + t = 2.692582404 + 1.5
t = 2.692582404 + 1.5

Combine like terms: 2.692582404 + 1.5 = 4.192582404
t = 4.192582404

Simplifying
t = 4.192582404


Subproblem 2
t + -1.5 = -2.692582404

Simplifying
t + -1.5 = -2.692582404

Reorder the terms:
-1.5 + t = -2.692582404

Solving
-1.5 + t = -2.692582404

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 = -2.692582404 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + t = -2.692582404 + 1.5
t = -2.692582404 + 1.5

Combine like terms: -2.692582404 + 1.5 = -1.192582404
t = -1.192582404

Simplifying
t = -1.192582404


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {4.192582404, -1.192582404}
Solution
t = {4.192582404, -1.192582404}

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