25t^2-40t=16

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Solution for 25t^2-40t=16 equation:


Simplifying
25t2 + -40t = 16

Reorder the terms:
-40t + 25t2 = 16

Solving
-40t + 25t2 = 16

Solving for variable 't'.

Reorder the terms:
-16 + -40t + 25t2 = 16 + -16

Combine like terms: 16 + -16 = 0
-16 + -40t + 25t2 = 0

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

Divide each side by '25'.
-0.64 + -1.6t + t2 = 0

Move the constant term to the right:

Add '0.64' to each side of the equation.
-0.64 + -1.6t + 0.64 + t2 = 0 + 0.64

Reorder the terms:
-0.64 + 0.64 + -1.6t + t2 = 0 + 0.64

Combine like terms: -0.64 + 0.64 = 0.00
0.00 + -1.6t + t2 = 0 + 0.64
-1.6t + t2 = 0 + 0.64

Combine like terms: 0 + 0.64 = 0.64
-1.6t + t2 = 0.64

The t term is -1.6t.  Take half its coefficient (-0.8).
Square it (0.64) and add it to both sides.

Add '0.64' to each side of the equation.
-1.6t + 0.64 + t2 = 0.64 + 0.64

Reorder the terms:
0.64 + -1.6t + t2 = 0.64 + 0.64

Combine like terms: 0.64 + 0.64 = 1.28
0.64 + -1.6t + t2 = 1.28

Factor a perfect square on the left side:
(t + -0.8)(t + -0.8) = 1.28

Calculate the square root of the right side: 1.13137085

Break this problem into two subproblems by setting 
(t + -0.8) equal to 1.13137085 and -1.13137085.

Subproblem 1

t + -0.8 = 1.13137085 Simplifying t + -0.8 = 1.13137085 Reorder the terms: -0.8 + t = 1.13137085 Solving -0.8 + t = 1.13137085 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + t = 1.13137085 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + t = 1.13137085 + 0.8 t = 1.13137085 + 0.8 Combine like terms: 1.13137085 + 0.8 = 1.93137085 t = 1.93137085 Simplifying t = 1.93137085

Subproblem 2

t + -0.8 = -1.13137085 Simplifying t + -0.8 = -1.13137085 Reorder the terms: -0.8 + t = -1.13137085 Solving -0.8 + t = -1.13137085 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + t = -1.13137085 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + t = -1.13137085 + 0.8 t = -1.13137085 + 0.8 Combine like terms: -1.13137085 + 0.8 = -0.33137085 t = -0.33137085 Simplifying t = -0.33137085

Solution

The solution to the problem is based on the solutions from the subproblems. t = {1.93137085, -0.33137085}

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