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Simplifying -16t2 + 88t + 80 = 2 Reorder the terms: 80 + 88t + -16t2 = 2 Solving 80 + 88t + -16t2 = 2 Solving for variable 't'. Reorder the terms: 80 + -2 + 88t + -16t2 = 2 + -2 Combine like terms: 80 + -2 = 78 78 + 88t + -16t2 = 2 + -2 Combine like terms: 2 + -2 = 0 78 + 88t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(39 + 44t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(39 + 44t + -8t2)' equal to zero and attempt to solve: Simplifying 39 + 44t + -8t2 = 0 Solving 39 + 44t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -4.875 + -5.5t + t2 = 0 Move the constant term to the right: Add '4.875' to each side of the equation. -4.875 + -5.5t + 4.875 + t2 = 0 + 4.875 Reorder the terms: -4.875 + 4.875 + -5.5t + t2 = 0 + 4.875 Combine like terms: -4.875 + 4.875 = 0.000 0.000 + -5.5t + t2 = 0 + 4.875 -5.5t + t2 = 0 + 4.875 Combine like terms: 0 + 4.875 = 4.875 -5.5t + t2 = 4.875 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 = 4.875 + 7.5625 Reorder the terms: 7.5625 + -5.5t + t2 = 4.875 + 7.5625 Combine like terms: 4.875 + 7.5625 = 12.4375 7.5625 + -5.5t + t2 = 12.4375 Factor a perfect square on the left side: (t + -2.75)(t + -2.75) = 12.4375 Calculate the square root of the right side: 3.526683995 Break this problem into two subproblems by setting (t + -2.75) equal to 3.526683995 and -3.526683995.Subproblem 1
t + -2.75 = 3.526683995 Simplifying t + -2.75 = 3.526683995 Reorder the terms: -2.75 + t = 3.526683995 Solving -2.75 + t = 3.526683995 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 = 3.526683995 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + t = 3.526683995 + 2.75 t = 3.526683995 + 2.75 Combine like terms: 3.526683995 + 2.75 = 6.276683995 t = 6.276683995 Simplifying t = 6.276683995Subproblem 2
t + -2.75 = -3.526683995 Simplifying t + -2.75 = -3.526683995 Reorder the terms: -2.75 + t = -3.526683995 Solving -2.75 + t = -3.526683995 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 = -3.526683995 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + t = -3.526683995 + 2.75 t = -3.526683995 + 2.75 Combine like terms: -3.526683995 + 2.75 = -0.776683995 t = -0.776683995 Simplifying t = -0.776683995Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.276683995, -0.776683995}Solution
t = {6.276683995, -0.776683995}
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