0=16t^2-96t-92

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Solution for 0=16t^2-96t-92 equation:


Simplifying
0 = 16t2 + -96t + -92

Reorder the terms:
0 = -92 + -96t + 16t2

Solving
0 = -92 + -96t + 16t2

Solving for variable 't'.

Combine like terms: 0 + 92 = 92
92 + 96t + -16t2 = -92 + -96t + 16t2 + 92 + 96t + -16t2

Reorder the terms:
92 + 96t + -16t2 = -92 + 92 + -96t + 96t + 16t2 + -16t2

Combine like terms: -92 + 92 = 0
92 + 96t + -16t2 = 0 + -96t + 96t + 16t2 + -16t2
92 + 96t + -16t2 = -96t + 96t + 16t2 + -16t2

Combine like terms: -96t + 96t = 0
92 + 96t + -16t2 = 0 + 16t2 + -16t2
92 + 96t + -16t2 = 16t2 + -16t2

Combine like terms: 16t2 + -16t2 = 0
92 + 96t + -16t2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(23 + 24t + -4t2) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(23 + 24t + -4t2)' equal to zero and attempt to solve: Simplifying 23 + 24t + -4t2 = 0 Solving 23 + 24t + -4t2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -5.75 + -6t + t2 = 0 Move the constant term to the right: Add '5.75' to each side of the equation. -5.75 + -6t + 5.75 + t2 = 0 + 5.75 Reorder the terms: -5.75 + 5.75 + -6t + t2 = 0 + 5.75 Combine like terms: -5.75 + 5.75 = 0.00 0.00 + -6t + t2 = 0 + 5.75 -6t + t2 = 0 + 5.75 Combine like terms: 0 + 5.75 = 5.75 -6t + t2 = 5.75 The t term is -6t. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6t + 9 + t2 = 5.75 + 9 Reorder the terms: 9 + -6t + t2 = 5.75 + 9 Combine like terms: 5.75 + 9 = 14.75 9 + -6t + t2 = 14.75 Factor a perfect square on the left side: (t + -3)(t + -3) = 14.75 Calculate the square root of the right side: 3.840572874 Break this problem into two subproblems by setting (t + -3) equal to 3.840572874 and -3.840572874.

Subproblem 1

t + -3 = 3.840572874 Simplifying t + -3 = 3.840572874 Reorder the terms: -3 + t = 3.840572874 Solving -3 + t = 3.840572874 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = 3.840572874 + 3 Combine like terms: -3 + 3 = 0 0 + t = 3.840572874 + 3 t = 3.840572874 + 3 Combine like terms: 3.840572874 + 3 = 6.840572874 t = 6.840572874 Simplifying t = 6.840572874

Subproblem 2

t + -3 = -3.840572874 Simplifying t + -3 = -3.840572874 Reorder the terms: -3 + t = -3.840572874 Solving -3 + t = -3.840572874 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = -3.840572874 + 3 Combine like terms: -3 + 3 = 0 0 + t = -3.840572874 + 3 t = -3.840572874 + 3 Combine like terms: -3.840572874 + 3 = -0.840572874 t = -0.840572874 Simplifying t = -0.840572874

Solution

The solution to the problem is based on the solutions from the subproblems. t = {6.840572874, -0.840572874}

Solution

t = {6.840572874, -0.840572874}

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