16t^2+10t-70=0

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Solution for 16t^2+10t-70=0 equation: 


Simplifying
16t2 + 10t + -70 = 0

Reorder the terms:
-70 + 10t + 16t2 = 0

Solving
-70 + 10t + 16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-35 + 5t + 8t2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-35 + 5t + 8t2)' equal to zero and attempt to solve:

Simplifying
-35 + 5t + 8t2 = 0

Solving
-35 + 5t + 8t2 = 0

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

Divide each side by '8'.
-4.375 + 0.625t + t2 = 0

Move the constant term to the right:

Add '4.375' to each side of the equation.
-4.375 + 0.625t + 4.375 + t2 = 0 + 4.375

Reorder the terms:
-4.375 + 4.375 + 0.625t + t2 = 0 + 4.375

Combine like terms: -4.375 + 4.375 = 0.000
0.000 + 0.625t + t2 = 0 + 4.375
0.625t + t2 = 0 + 4.375

Combine like terms: 0 + 4.375 = 4.375
0.625t + t2 = 4.375

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 = 4.375 + 0.09765625

Reorder the terms:
0.09765625 + 0.625t + t2 = 4.375 + 0.09765625

Combine like terms: 4.375 + 0.09765625 = 4.47265625
0.09765625 + 0.625t + t2 = 4.47265625

Factor a perfect square on the left side:
(t + 0.3125)(t + 0.3125) = 4.47265625

Calculate the square root of the right side: 2.114865539

Break this problem into two subproblems by setting 
(t + 0.3125) equal to 2.114865539 and -2.114865539.


Subproblem 1
t + 0.3125 = 2.114865539

Simplifying
t + 0.3125 = 2.114865539

Reorder the terms:
0.3125 + t = 2.114865539

Solving
0.3125 + t = 2.114865539

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 = 2.114865539 + -0.3125

Combine like terms: 0.3125 + -0.3125 = 0.0000
0.0000 + t = 2.114865539 + -0.3125
t = 2.114865539 + -0.3125

Combine like terms: 2.114865539 + -0.3125 = 1.802365539
t = 1.802365539

Simplifying
t = 1.802365539


Subproblem 2
t + 0.3125 = -2.114865539

Simplifying
t + 0.3125 = -2.114865539

Reorder the terms:
0.3125 + t = -2.114865539

Solving
0.3125 + t = -2.114865539

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 = -2.114865539 + -0.3125

Combine like terms: 0.3125 + -0.3125 = 0.0000
0.0000 + t = -2.114865539 + -0.3125
t = -2.114865539 + -0.3125

Combine like terms: -2.114865539 + -0.3125 = -2.427365539
t = -2.427365539

Simplifying
t = -2.427365539


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.802365539, -2.427365539}
Solution
t = {1.802365539, -2.427365539}

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