0=-16t^2+88t-88

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Solution for 0=-16t^2+88t-88 equation:


Simplifying
0 = -16t2 + 88t + -88

Reorder the terms:
0 = -88 + 88t + -16t2

Solving
0 = -88 + 88t + -16t2

Solving for variable 't'.

Combine like terms: 0 + 88 = 88
88 + -88t + 16t2 = -88 + 88t + -16t2 + 88 + -88t + 16t2

Reorder the terms:
88 + -88t + 16t2 = -88 + 88 + 88t + -88t + -16t2 + 16t2

Combine like terms: -88 + 88 = 0
88 + -88t + 16t2 = 0 + 88t + -88t + -16t2 + 16t2
88 + -88t + 16t2 = 88t + -88t + -16t2 + 16t2

Combine like terms: 88t + -88t = 0
88 + -88t + 16t2 = 0 + -16t2 + 16t2
88 + -88t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
88 + -88t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(11 + -11t + 2t2) = 0

Ignore the factor 8.

Subproblem 1

Set the factor '(11 + -11t + 2t2)' equal to zero and attempt to solve: Simplifying 11 + -11t + 2t2 = 0 Solving 11 + -11t + 2t2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 5.5 + -5.5t + t2 = 0 Move the constant term to the right: Add '-5.5' to each side of the equation. 5.5 + -5.5t + -5.5 + t2 = 0 + -5.5 Reorder the terms: 5.5 + -5.5 + -5.5t + t2 = 0 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + -5.5t + t2 = 0 + -5.5 -5.5t + t2 = 0 + -5.5 Combine like terms: 0 + -5.5 = -5.5 -5.5t + t2 = -5.5 The t term is -5.5t. Take half its coefficient (-2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. -5.5t + 7.5625 + t2 = -5.5 + 7.5625 Reorder the terms: 7.5625 + -5.5t + t2 = -5.5 + 7.5625 Combine like terms: -5.5 + 7.5625 = 2.0625 7.5625 + -5.5t + t2 = 2.0625 Factor a perfect square on the left side: (t + -2.75)(t + -2.75) = 2.0625 Calculate the square root of the right side: 1.436140662 Break this problem into two subproblems by setting (t + -2.75) equal to 1.436140662 and -1.436140662.

Subproblem 1

t + -2.75 = 1.436140662 Simplifying t + -2.75 = 1.436140662 Reorder the terms: -2.75 + t = 1.436140662 Solving -2.75 + t = 1.436140662 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + t = 1.436140662 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + t = 1.436140662 + 2.75 t = 1.436140662 + 2.75 Combine like terms: 1.436140662 + 2.75 = 4.186140662 t = 4.186140662 Simplifying t = 4.186140662

Subproblem 2

t + -2.75 = -1.436140662 Simplifying t + -2.75 = -1.436140662 Reorder the terms: -2.75 + t = -1.436140662 Solving -2.75 + t = -1.436140662 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + t = -1.436140662 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + t = -1.436140662 + 2.75 t = -1.436140662 + 2.75 Combine like terms: -1.436140662 + 2.75 = 1.313859338 t = 1.313859338 Simplifying t = 1.313859338

Solution

The solution to the problem is based on the solutions from the subproblems. t = {4.186140662, 1.313859338}

Solution

t = {4.186140662, 1.313859338}

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