-4t^2+56t+1=0

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Solution for -4t^2+56t+1=0 equation:


Simplifying
-4t2 + 56t + 1 = 0

Reorder the terms:
1 + 56t + -4t2 = 0

Solving
1 + 56t + -4t2 = 0

Solving for variable 't'.

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

Divide each side by '-4'.
-0.25 + -14t + t2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + -14t + 0.25 + t2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + -14t + t2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + -14t + t2 = 0 + 0.25
-14t + t2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
-14t + t2 = 0.25

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 = 0.25 + 49

Reorder the terms:
49 + -14t + t2 = 0.25 + 49

Combine like terms: 0.25 + 49 = 49.25
49 + -14t + t2 = 49.25

Factor a perfect square on the left side:
(t + -7)(t + -7) = 49.25

Calculate the square root of the right side: 7.017834424

Break this problem into two subproblems by setting 
(t + -7) equal to 7.017834424 and -7.017834424.

Subproblem 1

t + -7 = 7.017834424 Simplifying t + -7 = 7.017834424 Reorder the terms: -7 + t = 7.017834424 Solving -7 + t = 7.017834424 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 = 7.017834424 + 7 Combine like terms: -7 + 7 = 0 0 + t = 7.017834424 + 7 t = 7.017834424 + 7 Combine like terms: 7.017834424 + 7 = 14.017834424 t = 14.017834424 Simplifying t = 14.017834424

Subproblem 2

t + -7 = -7.017834424 Simplifying t + -7 = -7.017834424 Reorder the terms: -7 + t = -7.017834424 Solving -7 + t = -7.017834424 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 = -7.017834424 + 7 Combine like terms: -7 + 7 = 0 0 + t = -7.017834424 + 7 t = -7.017834424 + 7 Combine like terms: -7.017834424 + 7 = -0.017834424 t = -0.017834424 Simplifying t = -0.017834424

Solution

The solution to the problem is based on the solutions from the subproblems. t = {14.017834424, -0.017834424}

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