4t^2+56t-196=0

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Solution for 4t^2+56t-196=0 equation: 


Simplifying
4t2 + 56t + -196 = 0

Reorder the terms:
-196 + 56t + 4t2 = 0

Solving
-196 + 56t + 4t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-49 + 14t + t2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-49 + 14t + t2)' equal to zero and attempt to solve:

Simplifying
-49 + 14t + t2 = 0

Solving
-49 + 14t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '49' to each side of the equation.
-49 + 14t + 49 + t2 = 0 + 49

Reorder the terms:
-49 + 49 + 14t + t2 = 0 + 49

Combine like terms: -49 + 49 = 0
0 + 14t + t2 = 0 + 49
14t + t2 = 0 + 49

Combine like terms: 0 + 49 = 49
14t + t2 = 49

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 = 49 + 49

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

Combine like terms: 49 + 49 = 98
49 + 14t + t2 = 98

Factor a perfect square on the left side:
(t + 7)(t + 7) = 98

Calculate the square root of the right side: 9.899494937

Break this problem into two subproblems by setting 
(t + 7) equal to 9.899494937 and -9.899494937.


Subproblem 1
t + 7 = 9.899494937

Simplifying
t + 7 = 9.899494937

Reorder the terms:
7 + t = 9.899494937

Solving
7 + t = 9.899494937

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 = 9.899494937 + -7

Combine like terms: 7 + -7 = 0
0 + t = 9.899494937 + -7
t = 9.899494937 + -7

Combine like terms: 9.899494937 + -7 = 2.899494937
t = 2.899494937

Simplifying
t = 2.899494937


Subproblem 2
t + 7 = -9.899494937

Simplifying
t + 7 = -9.899494937

Reorder the terms:
7 + t = -9.899494937

Solving
7 + t = -9.899494937

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 = -9.899494937 + -7

Combine like terms: 7 + -7 = 0
0 + t = -9.899494937 + -7
t = -9.899494937 + -7

Combine like terms: -9.899494937 + -7 = -16.899494937
t = -16.899494937

Simplifying
t = -16.899494937


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.899494937, -16.899494937}
Solution
t = {2.899494937, -16.899494937}

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