7(t-6)7t=7(2t+2)-11

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Solution for 7(t-6)7t=7(2t+2)-11 equation:


Simplifying
7(t + -6) * 7t = 7(2t + 2) + -11

Reorder the terms:
7(-6 + t) * 7t = 7(2t + 2) + -11

Reorder the terms for easier multiplication:
7 * 7t(-6 + t) = 7(2t + 2) + -11

Multiply 7 * 7
49t(-6 + t) = 7(2t + 2) + -11
(-6 * 49t + t * 49t) = 7(2t + 2) + -11
(-294t + 49t2) = 7(2t + 2) + -11

Reorder the terms:
-294t + 49t2 = 7(2 + 2t) + -11
-294t + 49t2 = (2 * 7 + 2t * 7) + -11
-294t + 49t2 = (14 + 14t) + -11

Reorder the terms:
-294t + 49t2 = 14 + -11 + 14t

Combine like terms: 14 + -11 = 3
-294t + 49t2 = 3 + 14t

Solving
-294t + 49t2 = 3 + 14t

Solving for variable 't'.

Reorder the terms:
-3 + -294t + -14t + 49t2 = 3 + 14t + -3 + -14t

Combine like terms: -294t + -14t = -308t
-3 + -308t + 49t2 = 3 + 14t + -3 + -14t

Reorder the terms:
-3 + -308t + 49t2 = 3 + -3 + 14t + -14t

Combine like terms: 3 + -3 = 0
-3 + -308t + 49t2 = 0 + 14t + -14t
-3 + -308t + 49t2 = 14t + -14t

Combine like terms: 14t + -14t = 0
-3 + -308t + 49t2 = 0

Begin completing the square.  Divide all terms by
49 the coefficient of the squared term: 

Divide each side by '49'.
-0.0612244898 + -6.285714286t + t2 = 0

Move the constant term to the right:

Add '0.0612244898' to each side of the equation.
-0.0612244898 + -6.285714286t + 0.0612244898 + t2 = 0 + 0.0612244898

Reorder the terms:
-0.0612244898 + 0.0612244898 + -6.285714286t + t2 = 0 + 0.0612244898

Combine like terms: -0.0612244898 + 0.0612244898 = 0.0000000000
0.0000000000 + -6.285714286t + t2 = 0 + 0.0612244898
-6.285714286t + t2 = 0 + 0.0612244898

Combine like terms: 0 + 0.0612244898 = 0.0612244898
-6.285714286t + t2 = 0.0612244898

The t term is -6.285714286t.  Take half its coefficient (-3.142857143).
Square it (9.877551021) and add it to both sides.

Add '9.877551021' to each side of the equation.
-6.285714286t + 9.877551021 + t2 = 0.0612244898 + 9.877551021

Reorder the terms:
9.877551021 + -6.285714286t + t2 = 0.0612244898 + 9.877551021

Combine like terms: 0.0612244898 + 9.877551021 = 9.9387755108
9.877551021 + -6.285714286t + t2 = 9.9387755108

Factor a perfect square on the left side:
(t + -3.142857143)(t + -3.142857143) = 9.9387755108

Calculate the square root of the right side: 3.152582356

Break this problem into two subproblems by setting 
(t + -3.142857143) equal to 3.152582356 and -3.152582356.

Subproblem 1

t + -3.142857143 = 3.152582356 Simplifying t + -3.142857143 = 3.152582356 Reorder the terms: -3.142857143 + t = 3.152582356 Solving -3.142857143 + t = 3.152582356 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.142857143' to each side of the equation. -3.142857143 + 3.142857143 + t = 3.152582356 + 3.142857143 Combine like terms: -3.142857143 + 3.142857143 = 0.000000000 0.000000000 + t = 3.152582356 + 3.142857143 t = 3.152582356 + 3.142857143 Combine like terms: 3.152582356 + 3.142857143 = 6.295439499 t = 6.295439499 Simplifying t = 6.295439499

Subproblem 2

t + -3.142857143 = -3.152582356 Simplifying t + -3.142857143 = -3.152582356 Reorder the terms: -3.142857143 + t = -3.152582356 Solving -3.142857143 + t = -3.152582356 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.142857143' to each side of the equation. -3.142857143 + 3.142857143 + t = -3.152582356 + 3.142857143 Combine like terms: -3.142857143 + 3.142857143 = 0.000000000 0.000000000 + t = -3.152582356 + 3.142857143 t = -3.152582356 + 3.142857143 Combine like terms: -3.152582356 + 3.142857143 = -0.009725213 t = -0.009725213 Simplifying t = -0.009725213

Solution

The solution to the problem is based on the solutions from the subproblems. t = {6.295439499, -0.009725213}

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