t^2-28t=27

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Solution for t^2-28t=27 equation:


Simplifying
t2 + -28t = 27

Reorder the terms:
-28t + t2 = 27

Solving
-28t + t2 = 27

Solving for variable 't'.

Reorder the terms:
-27 + -28t + t2 = 27 + -27

Combine like terms: 27 + -27 = 0
-27 + -28t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '27' to each side of the equation.
-27 + -28t + 27 + t2 = 0 + 27

Reorder the terms:
-27 + 27 + -28t + t2 = 0 + 27

Combine like terms: -27 + 27 = 0
0 + -28t + t2 = 0 + 27
-28t + t2 = 0 + 27

Combine like terms: 0 + 27 = 27
-28t + t2 = 27

The t term is -28t.  Take half its coefficient (-14).
Square it (196) and add it to both sides.

Add '196' to each side of the equation.
-28t + 196 + t2 = 27 + 196

Reorder the terms:
196 + -28t + t2 = 27 + 196

Combine like terms: 27 + 196 = 223
196 + -28t + t2 = 223

Factor a perfect square on the left side:
(t + -14)(t + -14) = 223

Calculate the square root of the right side: 14.933184523

Break this problem into two subproblems by setting 
(t + -14) equal to 14.933184523 and -14.933184523.

Subproblem 1

t + -14 = 14.933184523 Simplifying t + -14 = 14.933184523 Reorder the terms: -14 + t = 14.933184523 Solving -14 + t = 14.933184523 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + t = 14.933184523 + 14 Combine like terms: -14 + 14 = 0 0 + t = 14.933184523 + 14 t = 14.933184523 + 14 Combine like terms: 14.933184523 + 14 = 28.933184523 t = 28.933184523 Simplifying t = 28.933184523

Subproblem 2

t + -14 = -14.933184523 Simplifying t + -14 = -14.933184523 Reorder the terms: -14 + t = -14.933184523 Solving -14 + t = -14.933184523 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + t = -14.933184523 + 14 Combine like terms: -14 + 14 = 0 0 + t = -14.933184523 + 14 t = -14.933184523 + 14 Combine like terms: -14.933184523 + 14 = -0.933184523 t = -0.933184523 Simplifying t = -0.933184523

Solution

The solution to the problem is based on the solutions from the subproblems. t = {28.933184523, -0.933184523}

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