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Simplifying -16t2 + 160t + 32 = 0 Reorder the terms: 32 + 160t + -16t2 = 0 Solving 32 + 160t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '16'. 16(2 + 10t + -1t2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(2 + 10t + -1t2)' equal to zero and attempt to solve: Simplifying 2 + 10t + -1t2 = 0 Solving 2 + 10t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -2 + -10t + t2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -10t + 2 + t2 = 0 + 2 Reorder the terms: -2 + 2 + -10t + t2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -10t + t2 = 0 + 2 -10t + t2 = 0 + 2 Combine like terms: 0 + 2 = 2 -10t + t2 = 2 The t term is -10t. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10t + 25 + t2 = 2 + 25 Reorder the terms: 25 + -10t + t2 = 2 + 25 Combine like terms: 2 + 25 = 27 25 + -10t + t2 = 27 Factor a perfect square on the left side: (t + -5)(t + -5) = 27 Calculate the square root of the right side: 5.196152423 Break this problem into two subproblems by setting (t + -5) equal to 5.196152423 and -5.196152423.Subproblem 1
t + -5 = 5.196152423 Simplifying t + -5 = 5.196152423 Reorder the terms: -5 + t = 5.196152423 Solving -5 + t = 5.196152423 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + t = 5.196152423 + 5 Combine like terms: -5 + 5 = 0 0 + t = 5.196152423 + 5 t = 5.196152423 + 5 Combine like terms: 5.196152423 + 5 = 10.196152423 t = 10.196152423 Simplifying t = 10.196152423Subproblem 2
t + -5 = -5.196152423 Simplifying t + -5 = -5.196152423 Reorder the terms: -5 + t = -5.196152423 Solving -5 + t = -5.196152423 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + t = -5.196152423 + 5 Combine like terms: -5 + 5 = 0 0 + t = -5.196152423 + 5 t = -5.196152423 + 5 Combine like terms: -5.196152423 + 5 = -0.196152423 t = -0.196152423 Simplifying t = -0.196152423Solution
The solution to the problem is based on the solutions from the subproblems. t = {10.196152423, -0.196152423}Solution
t = {10.196152423, -0.196152423}
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