35=70t-5t^2

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Solution for 35=70t-5t^2 equation: 


Simplifying
35 = 70t + -5t2

Solving
35 = 70t + -5t2

Solving for variable 't'.

Reorder the terms:
35 + -70t + 5t2 = 70t + -70t + -5t2 + 5t2

Combine like terms: 70t + -70t = 0
35 + -70t + 5t2 = 0 + -5t2 + 5t2
35 + -70t + 5t2 = -5t2 + 5t2

Combine like terms: -5t2 + 5t2 = 0
35 + -70t + 5t2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(7 + -14t + t2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(7 + -14t + t2)' equal to zero and attempt to solve:

Simplifying
7 + -14t + t2 = 0

Solving
7 + -14t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + -14t + -7 + t2 = 0 + -7

Reorder the terms:
7 + -7 + -14t + t2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -14t + t2 = 0 + -7
-14t + t2 = 0 + -7

Combine like terms: 0 + -7 = -7
-14t + t2 = -7

The t term is -14t.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14t + 49 + t2 = -7 + 49

Reorder the terms:
49 + -14t + t2 = -7 + 49

Combine like terms: -7 + 49 = 42
49 + -14t + t2 = 42

Factor a perfect square on the left side:
(t + -7)(t + -7) = 42

Calculate the square root of the right side: 6.480740698

Break this problem into two subproblems by setting 
(t + -7) equal to 6.480740698 and -6.480740698.


Subproblem 1
t + -7 = 6.480740698

Simplifying
t + -7 = 6.480740698

Reorder the terms:
-7 + t = 6.480740698

Solving
-7 + t = 6.480740698

Solving for variable 't'.

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

Add '7' to each side of the equation.
-7 + 7 + t = 6.480740698 + 7

Combine like terms: -7 + 7 = 0
0 + t = 6.480740698 + 7
t = 6.480740698 + 7

Combine like terms: 6.480740698 + 7 = 13.480740698
t = 13.480740698

Simplifying
t = 13.480740698


Subproblem 2
t + -7 = -6.480740698

Simplifying
t + -7 = -6.480740698

Reorder the terms:
-7 + t = -6.480740698

Solving
-7 + t = -6.480740698

Solving for variable 't'.

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

Add '7' to each side of the equation.
-7 + 7 + t = -6.480740698 + 7

Combine like terms: -7 + 7 = 0
0 + t = -6.480740698 + 7
t = -6.480740698 + 7

Combine like terms: -6.480740698 + 7 = 0.519259302
t = 0.519259302

Simplifying
t = 0.519259302


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {13.480740698, 0.519259302}
Solution
t = {13.480740698, 0.519259302}

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