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Simplifying 16t2 + 64t + -60 = 0 Reorder the terms: -60 + 64t + 16t2 = 0 Solving -60 + 64t + 16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4'. 4(-15 + 16t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-15 + 16t + 4t2)' equal to zero and attempt to solve: Simplifying -15 + 16t + 4t2 = 0 Solving -15 + 16t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3.75 + 4t + t2 = 0 Move the constant term to the right: Add '3.75' to each side of the equation. -3.75 + 4t + 3.75 + t2 = 0 + 3.75 Reorder the terms: -3.75 + 3.75 + 4t + t2 = 0 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + 4t + t2 = 0 + 3.75 4t + t2 = 0 + 3.75 Combine like terms: 0 + 3.75 = 3.75 4t + t2 = 3.75 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 = 3.75 + 4 Reorder the terms: 4 + 4t + t2 = 3.75 + 4 Combine like terms: 3.75 + 4 = 7.75 4 + 4t + t2 = 7.75 Factor a perfect square on the left side: (t + 2)(t + 2) = 7.75 Calculate the square root of the right side: 2.783882181 Break this problem into two subproblems by setting (t + 2) equal to 2.783882181 and -2.783882181.Subproblem 1
t + 2 = 2.783882181 Simplifying t + 2 = 2.783882181 Reorder the terms: 2 + t = 2.783882181 Solving 2 + t = 2.783882181 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 = 2.783882181 + -2 Combine like terms: 2 + -2 = 0 0 + t = 2.783882181 + -2 t = 2.783882181 + -2 Combine like terms: 2.783882181 + -2 = 0.783882181 t = 0.783882181 Simplifying t = 0.783882181Subproblem 2
t + 2 = -2.783882181 Simplifying t + 2 = -2.783882181 Reorder the terms: 2 + t = -2.783882181 Solving 2 + t = -2.783882181 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 = -2.783882181 + -2 Combine like terms: 2 + -2 = 0 0 + t = -2.783882181 + -2 t = -2.783882181 + -2 Combine like terms: -2.783882181 + -2 = -4.783882181 t = -4.783882181 Simplifying t = -4.783882181Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.783882181, -4.783882181}Solution
t = {0.783882181, -4.783882181}
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