(.5t-1)(.5t-1)=0

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Solution for (.5t-1)(.5t-1)=0 equation:


Simplifying
(0.5t + -1)(0.5t + -1) = 0

Reorder the terms:
(-1 + 0.5t)(0.5t + -1) = 0

Reorder the terms:
(-1 + 0.5t)(-1 + 0.5t) = 0

Multiply (-1 + 0.5t) * (-1 + 0.5t)
(-1(-1 + 0.5t) + 0.5t * (-1 + 0.5t)) = 0
((-1 * -1 + 0.5t * -1) + 0.5t * (-1 + 0.5t)) = 0
((1 + -0.5t) + 0.5t * (-1 + 0.5t)) = 0
(1 + -0.5t + (-1 * 0.5t + 0.5t * 0.5t)) = 0
(1 + -0.5t + (-0.5t + 0.25t2)) = 0

Combine like terms: -0.5t + -0.5t = -1t
(1 + -1t + 0.25t2) = 0

Solving
1 + -1t + 0.25t2 = 0

Solving for variable 't'.

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

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

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -4t + -4 + t2 = 0 + -4

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

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

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

The t term is -4t.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4t + 4 + t2 = -4 + 4

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

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

Factor a perfect square on the left side:
(t + -2)(t + -2) = 0

Calculate the square root of the right side: 0

Break this problem into two subproblems by setting 
(t + -2) equal to 0 and 0.

Subproblem 1

t + -2 = 0 Simplifying t + -2 = 0 Reorder the terms: -2 + t = 0 Solving -2 + t = 0 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = 0 + 2 Combine like terms: -2 + 2 = 0 0 + t = 0 + 2 t = 0 + 2 Combine like terms: 0 + 2 = 2 t = 2 Simplifying t = 2

Subproblem 2

t + -2 = 0 Simplifying t + -2 = 0 Reorder the terms: -2 + t = 0 Solving -2 + t = 0 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = 0 + 2 Combine like terms: -2 + 2 = 0 0 + t = 0 + 2 t = 0 + 2 Combine like terms: 0 + 2 = 2 t = 2 Simplifying t = 2

Solution

The solution to the problem is based on the solutions from the subproblems. t = {2, 2}

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