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Simplifying 0 = -16t2 + 16t + 92 Reorder the terms: 0 = 92 + 16t + -16t2 Solving 0 = 92 + 16t + -16t2 Solving for variable 't'. Combine like terms: 0 + -92 = -92 -92 + -16t + 16t2 = 92 + 16t + -16t2 + -92 + -16t + 16t2 Reorder the terms: -92 + -16t + 16t2 = 92 + -92 + 16t + -16t + -16t2 + 16t2 Combine like terms: 92 + -92 = 0 -92 + -16t + 16t2 = 0 + 16t + -16t + -16t2 + 16t2 -92 + -16t + 16t2 = 16t + -16t + -16t2 + 16t2 Combine like terms: 16t + -16t = 0 -92 + -16t + 16t2 = 0 + -16t2 + 16t2 -92 + -16t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -92 + -16t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-23 + -4t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-23 + -4t + 4t2)' equal to zero and attempt to solve: Simplifying -23 + -4t + 4t2 = 0 Solving -23 + -4t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -5.75 + -1t + t2 = 0 Move the constant term to the right: Add '5.75' to each side of the equation. -5.75 + -1t + 5.75 + t2 = 0 + 5.75 Reorder the terms: -5.75 + 5.75 + -1t + t2 = 0 + 5.75 Combine like terms: -5.75 + 5.75 = 0.00 0.00 + -1t + t2 = 0 + 5.75 -1t + t2 = 0 + 5.75 Combine like terms: 0 + 5.75 = 5.75 -1t + t2 = 5.75 The t term is -1t. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1t + 0.25 + t2 = 5.75 + 0.25 Reorder the terms: 0.25 + -1t + t2 = 5.75 + 0.25 Combine like terms: 5.75 + 0.25 = 6 0.25 + -1t + t2 = 6 Factor a perfect square on the left side: (t + -0.5)(t + -0.5) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (t + -0.5) equal to 2.449489743 and -2.449489743.Subproblem 1
t + -0.5 = 2.449489743 Simplifying t + -0.5 = 2.449489743 Reorder the terms: -0.5 + t = 2.449489743 Solving -0.5 + t = 2.449489743 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + t = 2.449489743 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + t = 2.449489743 + 0.5 t = 2.449489743 + 0.5 Combine like terms: 2.449489743 + 0.5 = 2.949489743 t = 2.949489743 Simplifying t = 2.949489743Subproblem 2
t + -0.5 = -2.449489743 Simplifying t + -0.5 = -2.449489743 Reorder the terms: -0.5 + t = -2.449489743 Solving -0.5 + t = -2.449489743 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + t = -2.449489743 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + t = -2.449489743 + 0.5 t = -2.449489743 + 0.5 Combine like terms: -2.449489743 + 0.5 = -1.949489743 t = -1.949489743 Simplifying t = -1.949489743Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.949489743, -1.949489743}Solution
t = {2.949489743, -1.949489743}
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