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Simplifying -16t2 + 64t + 120 = 0 Reorder the terms: 120 + 64t + -16t2 = 0 Solving 120 + 64t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '8'. 8(15 + 8t + -2t2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(15 + 8t + -2t2)' equal to zero and attempt to solve: Simplifying 15 + 8t + -2t2 = 0 Solving 15 + 8t + -2t2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -7.5 + -4t + t2 = 0 Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + -4t + 7.5 + t2 = 0 + 7.5 Reorder the terms: -7.5 + 7.5 + -4t + t2 = 0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + -4t + t2 = 0 + 7.5 -4t + t2 = 0 + 7.5 Combine like terms: 0 + 7.5 = 7.5 -4t + t2 = 7.5 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 = 7.5 + 4 Reorder the terms: 4 + -4t + t2 = 7.5 + 4 Combine like terms: 7.5 + 4 = 11.5 4 + -4t + t2 = 11.5 Factor a perfect square on the left side: (t + -2)(t + -2) = 11.5 Calculate the square root of the right side: 3.391164992 Break this problem into two subproblems by setting (t + -2) equal to 3.391164992 and -3.391164992.Subproblem 1
t + -2 = 3.391164992 Simplifying t + -2 = 3.391164992 Reorder the terms: -2 + t = 3.391164992 Solving -2 + t = 3.391164992 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 = 3.391164992 + 2 Combine like terms: -2 + 2 = 0 0 + t = 3.391164992 + 2 t = 3.391164992 + 2 Combine like terms: 3.391164992 + 2 = 5.391164992 t = 5.391164992 Simplifying t = 5.391164992Subproblem 2
t + -2 = -3.391164992 Simplifying t + -2 = -3.391164992 Reorder the terms: -2 + t = -3.391164992 Solving -2 + t = -3.391164992 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 = -3.391164992 + 2 Combine like terms: -2 + 2 = 0 0 + t = -3.391164992 + 2 t = -3.391164992 + 2 Combine like terms: -3.391164992 + 2 = -1.391164992 t = -1.391164992 Simplifying t = -1.391164992Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.391164992, -1.391164992}Solution
t = {5.391164992, -1.391164992}
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