6(6t^2+7t)+2(5t+16)+8t^2=

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Solution for 6(6t^2+7t)+2(5t+16)+8t^2= equation:


Simplifying
6(6t2 + 7t) + 2(5t + 16) + 8t2 = 0

Reorder the terms:
6(7t + 6t2) + 2(5t + 16) + 8t2 = 0
(7t * 6 + 6t2 * 6) + 2(5t + 16) + 8t2 = 0
(42t + 36t2) + 2(5t + 16) + 8t2 = 0

Reorder the terms:
42t + 36t2 + 2(16 + 5t) + 8t2 = 0
42t + 36t2 + (16 * 2 + 5t * 2) + 8t2 = 0
42t + 36t2 + (32 + 10t) + 8t2 = 0

Reorder the terms:
32 + 42t + 10t + 36t2 + 8t2 = 0

Combine like terms: 42t + 10t = 52t
32 + 52t + 36t2 + 8t2 = 0

Combine like terms: 36t2 + 8t2 = 44t2
32 + 52t + 44t2 = 0

Solving
32 + 52t + 44t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4'.
4(8 + 13t + 11t2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(8 + 13t + 11t2)' equal to zero and attempt to solve:

Simplifying
8 + 13t + 11t2 = 0

Solving
8 + 13t + 11t2 = 0

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

Divide each side by '11'.
0.7272727273 + 1.181818182t + t2 = 0

Move the constant term to the right:

Add '-0.7272727273' to each side of the equation.
0.7272727273 + 1.181818182t + -0.7272727273 + t2 = 0 + -0.7272727273

Reorder the terms:
0.7272727273 + -0.7272727273 + 1.181818182t + t2 = 0 + -0.7272727273

Combine like terms: 0.7272727273 + -0.7272727273 = 0.0000000000
0.0000000000 + 1.181818182t + t2 = 0 + -0.7272727273
1.181818182t + t2 = 0 + -0.7272727273

Combine like terms: 0 + -0.7272727273 = -0.7272727273
1.181818182t + t2 = -0.7272727273

The t term is 1.181818182t.  Take half its coefficient (0.590909091).
Square it (0.3491735538) and add it to both sides.

Add '0.3491735538' to each side of the equation.
1.181818182t + 0.3491735538 + t2 = -0.7272727273 + 0.3491735538

Reorder the terms:
0.3491735538 + 1.181818182t + t2 = -0.7272727273 + 0.3491735538

Combine like terms: -0.7272727273 + 0.3491735538 = -0.3780991735
0.3491735538 + 1.181818182t + t2 = -0.3780991735

Factor a perfect square on the left side:
(t + 0.590909091)(t + 0.590909091) = -0.3780991735

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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