16t^2+20t+6=10

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Solution for 16t^2+20t+6=10 equation: 


Simplifying
16t2 + 20t + 6 = 10

Reorder the terms:
6 + 20t + 16t2 = 10

Solving
6 + 20t + 16t2 = 10

Solving for variable 't'.

Reorder the terms:
6 + -10 + 20t + 16t2 = 10 + -10

Combine like terms: 6 + -10 = -4
-4 + 20t + 16t2 = 10 + -10

Combine like terms: 10 + -10 = 0
-4 + 20t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-1 + 5t + 4t2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-1 + 5t + 4t2)' equal to zero and attempt to solve:

Simplifying
-1 + 5t + 4t2 = 0

Solving
-1 + 5t + 4t2 = 0

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

Divide each side by '4'.
-0.25 + 1.25t + t2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + 1.25t + 0.25 + t2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + 1.25t + t2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + 1.25t + t2 = 0 + 0.25
1.25t + t2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
1.25t + t2 = 0.25

The t term is 1.25t.  Take half its coefficient (0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
1.25t + 0.390625 + t2 = 0.25 + 0.390625

Reorder the terms:
0.390625 + 1.25t + t2 = 0.25 + 0.390625

Combine like terms: 0.25 + 0.390625 = 0.640625
0.390625 + 1.25t + t2 = 0.640625

Factor a perfect square on the left side:
(t + 0.625)(t + 0.625) = 0.640625

Calculate the square root of the right side: 0.80039053

Break this problem into two subproblems by setting 
(t + 0.625) equal to 0.80039053 and -0.80039053.


Subproblem 1
t + 0.625 = 0.80039053

Simplifying
t + 0.625 = 0.80039053

Reorder the terms:
0.625 + t = 0.80039053

Solving
0.625 + t = 0.80039053

Solving for variable 't'.

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

Add '-0.625' to each side of the equation.
0.625 + -0.625 + t = 0.80039053 + -0.625

Combine like terms: 0.625 + -0.625 = 0.000
0.000 + t = 0.80039053 + -0.625
t = 0.80039053 + -0.625

Combine like terms: 0.80039053 + -0.625 = 0.17539053
t = 0.17539053

Simplifying
t = 0.17539053


Subproblem 2
t + 0.625 = -0.80039053

Simplifying
t + 0.625 = -0.80039053

Reorder the terms:
0.625 + t = -0.80039053

Solving
0.625 + t = -0.80039053

Solving for variable 't'.

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

Add '-0.625' to each side of the equation.
0.625 + -0.625 + t = -0.80039053 + -0.625

Combine like terms: 0.625 + -0.625 = 0.000
0.000 + t = -0.80039053 + -0.625
t = -0.80039053 + -0.625

Combine like terms: -0.80039053 + -0.625 = -1.42539053
t = -1.42539053

Simplifying
t = -1.42539053


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.17539053, -1.42539053}
Solution
t = {0.17539053, -1.42539053}

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