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Simplifying 6 = -16t2 + 88t + 26 Reorder the terms: 6 = 26 + 88t + -16t2 Solving 6 = 26 + 88t + -16t2 Solving for variable 't'. Combine like terms: 6 + -26 = -20 -20 + -88t + 16t2 = 26 + 88t + -16t2 + -26 + -88t + 16t2 Reorder the terms: -20 + -88t + 16t2 = 26 + -26 + 88t + -88t + -16t2 + 16t2 Combine like terms: 26 + -26 = 0 -20 + -88t + 16t2 = 0 + 88t + -88t + -16t2 + 16t2 -20 + -88t + 16t2 = 88t + -88t + -16t2 + 16t2 Combine like terms: 88t + -88t = 0 -20 + -88t + 16t2 = 0 + -16t2 + 16t2 -20 + -88t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -20 + -88t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-5 + -22t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-5 + -22t + 4t2)' equal to zero and attempt to solve: Simplifying -5 + -22t + 4t2 = 0 Solving -5 + -22t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.25 + -5.5t + t2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + -5.5t + 1.25 + t2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + -5.5t + t2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + -5.5t + t2 = 0 + 1.25 -5.5t + t2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 -5.5t + t2 = 1.25 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 = 1.25 + 7.5625 Reorder the terms: 7.5625 + -5.5t + t2 = 1.25 + 7.5625 Combine like terms: 1.25 + 7.5625 = 8.8125 7.5625 + -5.5t + t2 = 8.8125 Factor a perfect square on the left side: (t + -2.75)(t + -2.75) = 8.8125 Calculate the square root of the right side: 2.968585522 Break this problem into two subproblems by setting (t + -2.75) equal to 2.968585522 and -2.968585522.Subproblem 1
t + -2.75 = 2.968585522 Simplifying t + -2.75 = 2.968585522 Reorder the terms: -2.75 + t = 2.968585522 Solving -2.75 + t = 2.968585522 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 = 2.968585522 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + t = 2.968585522 + 2.75 t = 2.968585522 + 2.75 Combine like terms: 2.968585522 + 2.75 = 5.718585522 t = 5.718585522 Simplifying t = 5.718585522Subproblem 2
t + -2.75 = -2.968585522 Simplifying t + -2.75 = -2.968585522 Reorder the terms: -2.75 + t = -2.968585522 Solving -2.75 + t = -2.968585522 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 = -2.968585522 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + t = -2.968585522 + 2.75 t = -2.968585522 + 2.75 Combine like terms: -2.968585522 + 2.75 = -0.218585522 t = -0.218585522 Simplifying t = -0.218585522Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.718585522, -0.218585522}Solution
t = {5.718585522, -0.218585522}
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