140=16T^2+64T

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Solution for 140=16T^2+64T equation: 


Simplifying
140 = 16T2 + 64T

Reorder the terms:
140 = 64T + 16T2

Solving
140 = 64T + 16T2

Solving for variable 'T'.

Reorder the terms:
140 + -64T + -16T2 = 64T + -64T + 16T2 + -16T2

Combine like terms: 64T + -64T = 0
140 + -64T + -16T2 = 0 + 16T2 + -16T2
140 + -64T + -16T2 = 16T2 + -16T2

Combine like terms: 16T2 + -16T2 = 0
140 + -64T + -16T2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(35 + -16T + -4T2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(35 + -16T + -4T2)' equal to zero and attempt to solve:

Simplifying
35 + -16T + -4T2 = 0

Solving
35 + -16T + -4T2 = 0

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

Divide each side by '-4'.
-8.75 + 4T + T2 = 0

Move the constant term to the right:

Add '8.75' to each side of the equation.
-8.75 + 4T + 8.75 + T2 = 0 + 8.75

Reorder the terms:
-8.75 + 8.75 + 4T + T2 = 0 + 8.75

Combine like terms: -8.75 + 8.75 = 0.00
0.00 + 4T + T2 = 0 + 8.75
4T + T2 = 0 + 8.75

Combine like terms: 0 + 8.75 = 8.75
4T + T2 = 8.75

The T term is 4T.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4T + 4 + T2 = 8.75 + 4

Reorder the terms:
4 + 4T + T2 = 8.75 + 4

Combine like terms: 8.75 + 4 = 12.75
4 + 4T + T2 = 12.75

Factor a perfect square on the left side:
(T + 2)(T + 2) = 12.75

Calculate the square root of the right side: 3.570714214

Break this problem into two subproblems by setting 
(T + 2) equal to 3.570714214 and -3.570714214.


Subproblem 1
T + 2 = 3.570714214

Simplifying
T + 2 = 3.570714214

Reorder the terms:
2 + T = 3.570714214

Solving
2 + T = 3.570714214

Solving for variable 'T'.

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

Add '-2' to each side of the equation.
2 + -2 + T = 3.570714214 + -2

Combine like terms: 2 + -2 = 0
0 + T = 3.570714214 + -2
T = 3.570714214 + -2

Combine like terms: 3.570714214 + -2 = 1.570714214
T = 1.570714214

Simplifying
T = 1.570714214


Subproblem 2
T + 2 = -3.570714214

Simplifying
T + 2 = -3.570714214

Reorder the terms:
2 + T = -3.570714214

Solving
2 + T = -3.570714214

Solving for variable 'T'.

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

Add '-2' to each side of the equation.
2 + -2 + T = -3.570714214 + -2

Combine like terms: 2 + -2 = 0
0 + T = -3.570714214 + -2
T = -3.570714214 + -2

Combine like terms: -3.570714214 + -2 = -5.570714214
T = -5.570714214

Simplifying
T = -5.570714214


Solution
The solution to the problem is based on the solutions
from the subproblems.
T = {1.570714214, -5.570714214}
Solution
T = {1.570714214, -5.570714214}

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