-16t^2-44t+6=0

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Solution for -16t^2-44t+6=0 equation:


Simplifying
-16t2 + -44t + 6 = 0

Reorder the terms:
6 + -44t + -16t2 = 0

Solving
6 + -44t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -22t + -8t2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(3 + -22t + -8t2)' equal to zero and attempt to solve: Simplifying 3 + -22t + -8t2 = 0 Solving 3 + -22t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -0.375 + 2.75t + t2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + 2.75t + 0.375 + t2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + 2.75t + t2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + 2.75t + t2 = 0 + 0.375 2.75t + t2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 2.75t + t2 = 0.375 The t term is 2.75t. Take half its coefficient (1.375). Square it (1.890625) and add it to both sides. Add '1.890625' to each side of the equation. 2.75t + 1.890625 + t2 = 0.375 + 1.890625 Reorder the terms: 1.890625 + 2.75t + t2 = 0.375 + 1.890625 Combine like terms: 0.375 + 1.890625 = 2.265625 1.890625 + 2.75t + t2 = 2.265625 Factor a perfect square on the left side: (t + 1.375)(t + 1.375) = 2.265625 Calculate the square root of the right side: 1.505199322 Break this problem into two subproblems by setting (t + 1.375) equal to 1.505199322 and -1.505199322.

Subproblem 1

t + 1.375 = 1.505199322 Simplifying t + 1.375 = 1.505199322 Reorder the terms: 1.375 + t = 1.505199322 Solving 1.375 + t = 1.505199322 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.375' to each side of the equation. 1.375 + -1.375 + t = 1.505199322 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + t = 1.505199322 + -1.375 t = 1.505199322 + -1.375 Combine like terms: 1.505199322 + -1.375 = 0.130199322 t = 0.130199322 Simplifying t = 0.130199322

Subproblem 2

t + 1.375 = -1.505199322 Simplifying t + 1.375 = -1.505199322 Reorder the terms: 1.375 + t = -1.505199322 Solving 1.375 + t = -1.505199322 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.375' to each side of the equation. 1.375 + -1.375 + t = -1.505199322 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + t = -1.505199322 + -1.375 t = -1.505199322 + -1.375 Combine like terms: -1.505199322 + -1.375 = -2.880199322 t = -2.880199322 Simplifying t = -2.880199322

Solution

The solution to the problem is based on the solutions from the subproblems. t = {0.130199322, -2.880199322}

Solution

t = {0.130199322, -2.880199322}

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