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Simplifying -16t2 + -160t + -125 = 0 Reorder the terms: -125 + -160t + -16t2 = 0 Solving -125 + -160t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '-1'. -1(125 + 160t + 16t2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(125 + 160t + 16t2)' equal to zero and attempt to solve: Simplifying 125 + 160t + 16t2 = 0 Solving 125 + 160t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 7.8125 + 10t + t2 = 0 Move the constant term to the right: Add '-7.8125' to each side of the equation. 7.8125 + 10t + -7.8125 + t2 = 0 + -7.8125 Reorder the terms: 7.8125 + -7.8125 + 10t + t2 = 0 + -7.8125 Combine like terms: 7.8125 + -7.8125 = 0.0000 0.0000 + 10t + t2 = 0 + -7.8125 10t + t2 = 0 + -7.8125 Combine like terms: 0 + -7.8125 = -7.8125 10t + t2 = -7.8125 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 = -7.8125 + 25 Reorder the terms: 25 + 10t + t2 = -7.8125 + 25 Combine like terms: -7.8125 + 25 = 17.1875 25 + 10t + t2 = 17.1875 Factor a perfect square on the left side: (t + 5)(t + 5) = 17.1875 Calculate the square root of the right side: 4.145780988 Break this problem into two subproblems by setting (t + 5) equal to 4.145780988 and -4.145780988.Subproblem 1
t + 5 = 4.145780988 Simplifying t + 5 = 4.145780988 Reorder the terms: 5 + t = 4.145780988 Solving 5 + t = 4.145780988 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 = 4.145780988 + -5 Combine like terms: 5 + -5 = 0 0 + t = 4.145780988 + -5 t = 4.145780988 + -5 Combine like terms: 4.145780988 + -5 = -0.854219012 t = -0.854219012 Simplifying t = -0.854219012Subproblem 2
t + 5 = -4.145780988 Simplifying t + 5 = -4.145780988 Reorder the terms: 5 + t = -4.145780988 Solving 5 + t = -4.145780988 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 = -4.145780988 + -5 Combine like terms: 5 + -5 = 0 0 + t = -4.145780988 + -5 t = -4.145780988 + -5 Combine like terms: -4.145780988 + -5 = -9.145780988 t = -9.145780988 Simplifying t = -9.145780988Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.854219012, -9.145780988}Solution
t = {-0.854219012, -9.145780988}
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