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Simplifying -16t2 + 64t + 560 = 0 Reorder the terms: 560 + 64t + -16t2 = 0 Solving 560 + 64t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '16'. 16(35 + 4t + -1t2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(35 + 4t + -1t2)' equal to zero and attempt to solve: Simplifying 35 + 4t + -1t2 = 0 Solving 35 + 4t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -35 + -4t + t2 = 0 Move the constant term to the right: Add '35' to each side of the equation. -35 + -4t + 35 + t2 = 0 + 35 Reorder the terms: -35 + 35 + -4t + t2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + -4t + t2 = 0 + 35 -4t + t2 = 0 + 35 Combine like terms: 0 + 35 = 35 -4t + t2 = 35 The t term is -4t. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4t + 4 + t2 = 35 + 4 Reorder the terms: 4 + -4t + t2 = 35 + 4 Combine like terms: 35 + 4 = 39 4 + -4t + t2 = 39 Factor a perfect square on the left side: (t + -2)(t + -2) = 39 Calculate the square root of the right side: 6.244997998 Break this problem into two subproblems by setting (t + -2) equal to 6.244997998 and -6.244997998.Subproblem 1
t + -2 = 6.244997998 Simplifying t + -2 = 6.244997998 Reorder the terms: -2 + t = 6.244997998 Solving -2 + t = 6.244997998 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = 6.244997998 + 2 Combine like terms: -2 + 2 = 0 0 + t = 6.244997998 + 2 t = 6.244997998 + 2 Combine like terms: 6.244997998 + 2 = 8.244997998 t = 8.244997998 Simplifying t = 8.244997998Subproblem 2
t + -2 = -6.244997998 Simplifying t + -2 = -6.244997998 Reorder the terms: -2 + t = -6.244997998 Solving -2 + t = -6.244997998 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = -6.244997998 + 2 Combine like terms: -2 + 2 = 0 0 + t = -6.244997998 + 2 t = -6.244997998 + 2 Combine like terms: -6.244997998 + 2 = -4.244997998 t = -4.244997998 Simplifying t = -4.244997998Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.244997998, -4.244997998}Solution
t = {8.244997998, -4.244997998}
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