12=25t-4t^2

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Solution for 12=25t-4t^2 equation:


Simplifying
12 = 25t + -4t2

Solving
12 = 25t + -4t2

Solving for variable 't'.

Reorder the terms:
12 + -25t + 4t2 = 25t + -25t + -4t2 + 4t2

Combine like terms: 25t + -25t = 0
12 + -25t + 4t2 = 0 + -4t2 + 4t2
12 + -25t + 4t2 = -4t2 + 4t2

Combine like terms: -4t2 + 4t2 = 0
12 + -25t + 4t2 = 0

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

Divide each side by '4'.
3 + -6.25t + t2 = 0

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -6.25t + -3 + t2 = 0 + -3

Reorder the terms:
3 + -3 + -6.25t + t2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -6.25t + t2 = 0 + -3
-6.25t + t2 = 0 + -3

Combine like terms: 0 + -3 = -3
-6.25t + t2 = -3

The t term is -6.25t.  Take half its coefficient (-3.125).
Square it (9.765625) and add it to both sides.

Add '9.765625' to each side of the equation.
-6.25t + 9.765625 + t2 = -3 + 9.765625

Reorder the terms:
9.765625 + -6.25t + t2 = -3 + 9.765625

Combine like terms: -3 + 9.765625 = 6.765625
9.765625 + -6.25t + t2 = 6.765625

Factor a perfect square on the left side:
(t + -3.125)(t + -3.125) = 6.765625

Calculate the square root of the right side: 2.601081506

Break this problem into two subproblems by setting 
(t + -3.125) equal to 2.601081506 and -2.601081506.

Subproblem 1

t + -3.125 = 2.601081506 Simplifying t + -3.125 = 2.601081506 Reorder the terms: -3.125 + t = 2.601081506 Solving -3.125 + t = 2.601081506 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + t = 2.601081506 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + t = 2.601081506 + 3.125 t = 2.601081506 + 3.125 Combine like terms: 2.601081506 + 3.125 = 5.726081506 t = 5.726081506 Simplifying t = 5.726081506

Subproblem 2

t + -3.125 = -2.601081506 Simplifying t + -3.125 = -2.601081506 Reorder the terms: -3.125 + t = -2.601081506 Solving -3.125 + t = -2.601081506 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + t = -2.601081506 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + t = -2.601081506 + 3.125 t = -2.601081506 + 3.125 Combine like terms: -2.601081506 + 3.125 = 0.523918494 t = 0.523918494 Simplifying t = 0.523918494

Solution

The solution to the problem is based on the solutions from the subproblems. t = {5.726081506, 0.523918494}

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