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Simplifying 110 = 16t2 + 48t Reorder the terms: 110 = 48t + 16t2 Solving 110 = 48t + 16t2 Solving for variable 't'. Reorder the terms: 110 + -48t + -16t2 = 48t + -48t + 16t2 + -16t2 Combine like terms: 48t + -48t = 0 110 + -48t + -16t2 = 0 + 16t2 + -16t2 110 + -48t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 110 + -48t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(55 + -24t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(55 + -24t + -8t2)' equal to zero and attempt to solve: Simplifying 55 + -24t + -8t2 = 0 Solving 55 + -24t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -6.875 + 3t + t2 = 0 Move the constant term to the right: Add '6.875' to each side of the equation. -6.875 + 3t + 6.875 + t2 = 0 + 6.875 Reorder the terms: -6.875 + 6.875 + 3t + t2 = 0 + 6.875 Combine like terms: -6.875 + 6.875 = 0.000 0.000 + 3t + t2 = 0 + 6.875 3t + t2 = 0 + 6.875 Combine like terms: 0 + 6.875 = 6.875 3t + t2 = 6.875 The t term is 3t. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3t + 2.25 + t2 = 6.875 + 2.25 Reorder the terms: 2.25 + 3t + t2 = 6.875 + 2.25 Combine like terms: 6.875 + 2.25 = 9.125 2.25 + 3t + t2 = 9.125 Factor a perfect square on the left side: (t + 1.5)(t + 1.5) = 9.125 Calculate the square root of the right side: 3.020761493 Break this problem into two subproblems by setting (t + 1.5) equal to 3.020761493 and -3.020761493.Subproblem 1
t + 1.5 = 3.020761493 Simplifying t + 1.5 = 3.020761493 Reorder the terms: 1.5 + t = 3.020761493 Solving 1.5 + t = 3.020761493 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + t = 3.020761493 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + t = 3.020761493 + -1.5 t = 3.020761493 + -1.5 Combine like terms: 3.020761493 + -1.5 = 1.520761493 t = 1.520761493 Simplifying t = 1.520761493Subproblem 2
t + 1.5 = -3.020761493 Simplifying t + 1.5 = -3.020761493 Reorder the terms: 1.5 + t = -3.020761493 Solving 1.5 + t = -3.020761493 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + t = -3.020761493 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + t = -3.020761493 + -1.5 t = -3.020761493 + -1.5 Combine like terms: -3.020761493 + -1.5 = -4.520761493 t = -4.520761493 Simplifying t = -4.520761493Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.520761493, -4.520761493}Solution
t = {1.520761493, -4.520761493}
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