-16t^2+88t+8=0

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Solution for -16t^2+88t+8=0 equation:


Simplifying
-16t2 + 88t + 8 = 0

Reorder the terms:
8 + 88t + -16t2 = 0

Solving
8 + 88t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '8'.
8(1 + 11t + -2t2) = 0

Ignore the factor 8.

Subproblem 1

Set the factor '(1 + 11t + -2t2)' equal to zero and attempt to solve: Simplifying 1 + 11t + -2t2 = 0 Solving 1 + 11t + -2t2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -0.5 + -5.5t + t2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -5.5t + 0.5 + t2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -5.5t + t2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -5.5t + t2 = 0 + 0.5 -5.5t + t2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -5.5t + t2 = 0.5 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 = 0.5 + 7.5625 Reorder the terms: 7.5625 + -5.5t + t2 = 0.5 + 7.5625 Combine like terms: 0.5 + 7.5625 = 8.0625 7.5625 + -5.5t + t2 = 8.0625 Factor a perfect square on the left side: (t + -2.75)(t + -2.75) = 8.0625 Calculate the square root of the right side: 2.839454173 Break this problem into two subproblems by setting (t + -2.75) equal to 2.839454173 and -2.839454173.

Subproblem 1

t + -2.75 = 2.839454173 Simplifying t + -2.75 = 2.839454173 Reorder the terms: -2.75 + t = 2.839454173 Solving -2.75 + t = 2.839454173 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 = 2.839454173 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + t = 2.839454173 + 2.75 t = 2.839454173 + 2.75 Combine like terms: 2.839454173 + 2.75 = 5.589454173 t = 5.589454173 Simplifying t = 5.589454173

Subproblem 2

t + -2.75 = -2.839454173 Simplifying t + -2.75 = -2.839454173 Reorder the terms: -2.75 + t = -2.839454173 Solving -2.75 + t = -2.839454173 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 = -2.839454173 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + t = -2.839454173 + 2.75 t = -2.839454173 + 2.75 Combine like terms: -2.839454173 + 2.75 = -0.089454173 t = -0.089454173 Simplifying t = -0.089454173

Solution

The solution to the problem is based on the solutions from the subproblems. t = {5.589454173, -0.089454173}

Solution

t = {5.589454173, -0.089454173}

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