49=16t^2+56t

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Solution for 49=16t^2+56t equation:


Simplifying
49 = 16t2 + 56t

Reorder the terms:
49 = 56t + 16t2

Solving
49 = 56t + 16t2

Solving for variable 't'.

Reorder the terms:
49 + -56t + -16t2 = 56t + -56t + 16t2 + -16t2

Combine like terms: 56t + -56t = 0
49 + -56t + -16t2 = 0 + 16t2 + -16t2
49 + -56t + -16t2 = 16t2 + -16t2

Combine like terms: 16t2 + -16t2 = 0
49 + -56t + -16t2 = 0

Begin completing the square.  Divide all terms by
-16 the coefficient of the squared term: 

Divide each side by '-16'.
-3.0625 + 3.5t + t2 = 0

Move the constant term to the right:

Add '3.0625' to each side of the equation.
-3.0625 + 3.5t + 3.0625 + t2 = 0 + 3.0625

Reorder the terms:
-3.0625 + 3.0625 + 3.5t + t2 = 0 + 3.0625

Combine like terms: -3.0625 + 3.0625 = 0.0000
0.0000 + 3.5t + t2 = 0 + 3.0625
3.5t + t2 = 0 + 3.0625

Combine like terms: 0 + 3.0625 = 3.0625
3.5t + t2 = 3.0625

The t term is 3.5t.  Take half its coefficient (1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
3.5t + 3.0625 + t2 = 3.0625 + 3.0625

Reorder the terms:
3.0625 + 3.5t + t2 = 3.0625 + 3.0625

Combine like terms: 3.0625 + 3.0625 = 6.125
3.0625 + 3.5t + t2 = 6.125

Factor a perfect square on the left side:
(t + 1.75)(t + 1.75) = 6.125

Calculate the square root of the right side: 2.474873734

Break this problem into two subproblems by setting 
(t + 1.75) equal to 2.474873734 and -2.474873734.

Subproblem 1

t + 1.75 = 2.474873734 Simplifying t + 1.75 = 2.474873734 Reorder the terms: 1.75 + t = 2.474873734 Solving 1.75 + t = 2.474873734 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + t = 2.474873734 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + t = 2.474873734 + -1.75 t = 2.474873734 + -1.75 Combine like terms: 2.474873734 + -1.75 = 0.724873734 t = 0.724873734 Simplifying t = 0.724873734

Subproblem 2

t + 1.75 = -2.474873734 Simplifying t + 1.75 = -2.474873734 Reorder the terms: 1.75 + t = -2.474873734 Solving 1.75 + t = -2.474873734 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + t = -2.474873734 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + t = -2.474873734 + -1.75 t = -2.474873734 + -1.75 Combine like terms: -2.474873734 + -1.75 = -4.224873734 t = -4.224873734 Simplifying t = -4.224873734

Solution

The solution to the problem is based on the solutions from the subproblems. t = {0.724873734, -4.224873734}

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