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Simplifying 0 = -16t2 + 8t + 96 Reorder the terms: 0 = 96 + 8t + -16t2 Solving 0 = 96 + 8t + -16t2 Solving for variable 't'. Combine like terms: 0 + -96 = -96 -96 + -8t + 16t2 = 96 + 8t + -16t2 + -96 + -8t + 16t2 Reorder the terms: -96 + -8t + 16t2 = 96 + -96 + 8t + -8t + -16t2 + 16t2 Combine like terms: 96 + -96 = 0 -96 + -8t + 16t2 = 0 + 8t + -8t + -16t2 + 16t2 -96 + -8t + 16t2 = 8t + -8t + -16t2 + 16t2 Combine like terms: 8t + -8t = 0 -96 + -8t + 16t2 = 0 + -16t2 + 16t2 -96 + -8t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -96 + -8t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-12 + -1t + 2t2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-12 + -1t + 2t2)' equal to zero and attempt to solve: Simplifying -12 + -1t + 2t2 = 0 Solving -12 + -1t + 2t2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -6 + -0.5t + t2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -0.5t + 6 + t2 = 0 + 6 Reorder the terms: -6 + 6 + -0.5t + t2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -0.5t + t2 = 0 + 6 -0.5t + t2 = 0 + 6 Combine like terms: 0 + 6 = 6 -0.5t + t2 = 6 The t term is -0.5t. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5t + 0.0625 + t2 = 6 + 0.0625 Reorder the terms: 0.0625 + -0.5t + t2 = 6 + 0.0625 Combine like terms: 6 + 0.0625 = 6.0625 0.0625 + -0.5t + t2 = 6.0625 Factor a perfect square on the left side: (t + -0.25)(t + -0.25) = 6.0625 Calculate the square root of the right side: 2.46221445 Break this problem into two subproblems by setting (t + -0.25) equal to 2.46221445 and -2.46221445.Subproblem 1
t + -0.25 = 2.46221445 Simplifying t + -0.25 = 2.46221445 Reorder the terms: -0.25 + t = 2.46221445 Solving -0.25 + t = 2.46221445 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + t = 2.46221445 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + t = 2.46221445 + 0.25 t = 2.46221445 + 0.25 Combine like terms: 2.46221445 + 0.25 = 2.71221445 t = 2.71221445 Simplifying t = 2.71221445Subproblem 2
t + -0.25 = -2.46221445 Simplifying t + -0.25 = -2.46221445 Reorder the terms: -0.25 + t = -2.46221445 Solving -0.25 + t = -2.46221445 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + t = -2.46221445 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + t = -2.46221445 + 0.25 t = -2.46221445 + 0.25 Combine like terms: -2.46221445 + 0.25 = -2.21221445 t = -2.21221445 Simplifying t = -2.21221445Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.71221445, -2.21221445}Solution
t = {2.71221445, -2.21221445}
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