0=-16t^2-80t+4

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Solution for 0=-16t^2-80t+4 equation:


Simplifying
0 = -16t2 + -80t + 4

Reorder the terms:
0 = 4 + -80t + -16t2

Solving
0 = 4 + -80t + -16t2

Solving for variable 't'.

Combine like terms: 0 + -4 = -4
-4 + 80t + 16t2 = 4 + -80t + -16t2 + -4 + 80t + 16t2

Reorder the terms:
-4 + 80t + 16t2 = 4 + -4 + -80t + 80t + -16t2 + 16t2

Combine like terms: 4 + -4 = 0
-4 + 80t + 16t2 = 0 + -80t + 80t + -16t2 + 16t2
-4 + 80t + 16t2 = -80t + 80t + -16t2 + 16t2

Combine like terms: -80t + 80t = 0
-4 + 80t + 16t2 = 0 + -16t2 + 16t2
-4 + 80t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-4 + 80t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-1 + 20t + 4t2) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(-1 + 20t + 4t2)' equal to zero and attempt to solve: Simplifying -1 + 20t + 4t2 = 0 Solving -1 + 20t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.25 + 5t + t2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + 5t + 0.25 + t2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + 5t + t2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + 5t + t2 = 0 + 0.25 5t + t2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 5t + t2 = 0.25 The t term is 5t. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5t + 6.25 + t2 = 0.25 + 6.25 Reorder the terms: 6.25 + 5t + t2 = 0.25 + 6.25 Combine like terms: 0.25 + 6.25 = 6.5 6.25 + 5t + t2 = 6.5 Factor a perfect square on the left side: (t + 2.5)(t + 2.5) = 6.5 Calculate the square root of the right side: 2.549509757 Break this problem into two subproblems by setting (t + 2.5) equal to 2.549509757 and -2.549509757.

Subproblem 1

t + 2.5 = 2.549509757 Simplifying t + 2.5 = 2.549509757 Reorder the terms: 2.5 + t = 2.549509757 Solving 2.5 + t = 2.549509757 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + t = 2.549509757 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + t = 2.549509757 + -2.5 t = 2.549509757 + -2.5 Combine like terms: 2.549509757 + -2.5 = 0.049509757 t = 0.049509757 Simplifying t = 0.049509757

Subproblem 2

t + 2.5 = -2.549509757 Simplifying t + 2.5 = -2.549509757 Reorder the terms: 2.5 + t = -2.549509757 Solving 2.5 + t = -2.549509757 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + t = -2.549509757 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + t = -2.549509757 + -2.5 t = -2.549509757 + -2.5 Combine like terms: -2.549509757 + -2.5 = -5.049509757 t = -5.049509757 Simplifying t = -5.049509757

Solution

The solution to the problem is based on the solutions from the subproblems. t = {0.049509757, -5.049509757}

Solution

t = {0.049509757, -5.049509757}

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