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Simplifying -16t2 + 96t + 64 = 0 Reorder the terms: 64 + 96t + -16t2 = 0 Solving 64 + 96t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '16'. 16(4 + 6t + -1t2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(4 + 6t + -1t2)' equal to zero and attempt to solve: Simplifying 4 + 6t + -1t2 = 0 Solving 4 + 6t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -4 + -6t + t2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -6t + 4 + t2 = 0 + 4 Reorder the terms: -4 + 4 + -6t + t2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -6t + t2 = 0 + 4 -6t + t2 = 0 + 4 Combine like terms: 0 + 4 = 4 -6t + t2 = 4 The t term is -6t. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6t + 9 + t2 = 4 + 9 Reorder the terms: 9 + -6t + t2 = 4 + 9 Combine like terms: 4 + 9 = 13 9 + -6t + t2 = 13 Factor a perfect square on the left side: (t + -3)(t + -3) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (t + -3) equal to 3.605551275 and -3.605551275.Subproblem 1
t + -3 = 3.605551275 Simplifying t + -3 = 3.605551275 Reorder the terms: -3 + t = 3.605551275 Solving -3 + t = 3.605551275 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = 3.605551275 + 3 Combine like terms: -3 + 3 = 0 0 + t = 3.605551275 + 3 t = 3.605551275 + 3 Combine like terms: 3.605551275 + 3 = 6.605551275 t = 6.605551275 Simplifying t = 6.605551275Subproblem 2
t + -3 = -3.605551275 Simplifying t + -3 = -3.605551275 Reorder the terms: -3 + t = -3.605551275 Solving -3 + t = -3.605551275 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = -3.605551275 + 3 Combine like terms: -3 + 3 = 0 0 + t = -3.605551275 + 3 t = -3.605551275 + 3 Combine like terms: -3.605551275 + 3 = -0.605551275 t = -0.605551275 Simplifying t = -0.605551275Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.605551275, -0.605551275}Solution
t = {6.605551275, -0.605551275}
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