40=16t^2+10t

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Solution for 40=16t^2+10t equation: 


Simplifying
40 = 16t2 + 10t

Reorder the terms:
40 = 10t + 16t2

Solving
40 = 10t + 16t2

Solving for variable 't'.

Reorder the terms:
40 + -10t + -16t2 = 10t + -10t + 16t2 + -16t2

Combine like terms: 10t + -10t = 0
40 + -10t + -16t2 = 0 + 16t2 + -16t2
40 + -10t + -16t2 = 16t2 + -16t2

Combine like terms: 16t2 + -16t2 = 0
40 + -10t + -16t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(20 + -5t + -8t2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(20 + -5t + -8t2)' equal to zero and attempt to solve:

Simplifying
20 + -5t + -8t2 = 0

Solving
20 + -5t + -8t2 = 0

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
-2.5 + 0.625t + t2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + 0.625t + 2.5 + t2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + 0.625t + t2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + 0.625t + t2 = 0 + 2.5
0.625t + t2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
0.625t + t2 = 2.5

The t term is 0.625t.  Take half its coefficient (0.3125).
Square it (0.09765625) and add it to both sides.

Add '0.09765625' to each side of the equation.
0.625t + 0.09765625 + t2 = 2.5 + 0.09765625

Reorder the terms:
0.09765625 + 0.625t + t2 = 2.5 + 0.09765625

Combine like terms: 2.5 + 0.09765625 = 2.59765625
0.09765625 + 0.625t + t2 = 2.59765625

Factor a perfect square on the left side:
(t + 0.3125)(t + 0.3125) = 2.59765625

Calculate the square root of the right side: 1.61172462

Break this problem into two subproblems by setting 
(t + 0.3125) equal to 1.61172462 and -1.61172462.


Subproblem 1
t + 0.3125 = 1.61172462

Simplifying
t + 0.3125 = 1.61172462

Reorder the terms:
0.3125 + t = 1.61172462

Solving
0.3125 + t = 1.61172462

Solving for variable 't'.

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

Add '-0.3125' to each side of the equation.
0.3125 + -0.3125 + t = 1.61172462 + -0.3125

Combine like terms: 0.3125 + -0.3125 = 0.0000
0.0000 + t = 1.61172462 + -0.3125
t = 1.61172462 + -0.3125

Combine like terms: 1.61172462 + -0.3125 = 1.29922462
t = 1.29922462

Simplifying
t = 1.29922462


Subproblem 2
t + 0.3125 = -1.61172462

Simplifying
t + 0.3125 = -1.61172462

Reorder the terms:
0.3125 + t = -1.61172462

Solving
0.3125 + t = -1.61172462

Solving for variable 't'.

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

Add '-0.3125' to each side of the equation.
0.3125 + -0.3125 + t = -1.61172462 + -0.3125

Combine like terms: 0.3125 + -0.3125 = 0.0000
0.0000 + t = -1.61172462 + -0.3125
t = -1.61172462 + -0.3125

Combine like terms: -1.61172462 + -0.3125 = -1.92422462
t = -1.92422462

Simplifying
t = -1.92422462


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.29922462, -1.92422462}
Solution
t = {1.29922462, -1.92422462}

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