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Simplifying 120 = 10t + 16t2 Solving 120 = 10t + 16t2 Solving for variable 't'. Reorder the terms: 120 + -10t + -16t2 = 10t + -10t + 16t2 + -16t2 Combine like terms: 10t + -10t = 0 120 + -10t + -16t2 = 0 + 16t2 + -16t2 120 + -10t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 120 + -10t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(60 + -5t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(60 + -5t + -8t2)' equal to zero and attempt to solve: Simplifying 60 + -5t + -8t2 = 0 Solving 60 + -5t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -7.5 + 0.625t + t2 = 0 Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + 0.625t + 7.5 + t2 = 0 + 7.5 Reorder the terms: -7.5 + 7.5 + 0.625t + t2 = 0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + 0.625t + t2 = 0 + 7.5 0.625t + t2 = 0 + 7.5 Combine like terms: 0 + 7.5 = 7.5 0.625t + t2 = 7.5 The t term is 0.625t. Take half its coefficient (0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. 0.625t + 0.09765625 + t2 = 7.5 + 0.09765625 Reorder the terms: 0.09765625 + 0.625t + t2 = 7.5 + 0.09765625 Combine like terms: 7.5 + 0.09765625 = 7.59765625 0.09765625 + 0.625t + t2 = 7.59765625 Factor a perfect square on the left side: (t + 0.3125)(t + 0.3125) = 7.59765625 Calculate the square root of the right side: 2.756384634 Break this problem into two subproblems by setting (t + 0.3125) equal to 2.756384634 and -2.756384634.Subproblem 1
t + 0.3125 = 2.756384634 Simplifying t + 0.3125 = 2.756384634 Reorder the terms: 0.3125 + t = 2.756384634 Solving 0.3125 + t = 2.756384634 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.3125' to each side of the equation. 0.3125 + -0.3125 + t = 2.756384634 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + t = 2.756384634 + -0.3125 t = 2.756384634 + -0.3125 Combine like terms: 2.756384634 + -0.3125 = 2.443884634 t = 2.443884634 Simplifying t = 2.443884634Subproblem 2
t + 0.3125 = -2.756384634 Simplifying t + 0.3125 = -2.756384634 Reorder the terms: 0.3125 + t = -2.756384634 Solving 0.3125 + t = -2.756384634 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.3125' to each side of the equation. 0.3125 + -0.3125 + t = -2.756384634 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + t = -2.756384634 + -0.3125 t = -2.756384634 + -0.3125 Combine like terms: -2.756384634 + -0.3125 = -3.068884634 t = -3.068884634 Simplifying t = -3.068884634Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.443884634, -3.068884634}Solution
t = {2.443884634, -3.068884634}
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