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Simplifying -16t2 + 64t + 48 = 0 Reorder the terms: 48 + 64t + -16t2 = 0 Solving 48 + 64t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '16'. 16(3 + 4t + -1t2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(3 + 4t + -1t2)' equal to zero and attempt to solve: Simplifying 3 + 4t + -1t2 = 0 Solving 3 + 4t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -3 + -4t + t2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -4t + 3 + t2 = 0 + 3 Reorder the terms: -3 + 3 + -4t + t2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4t + t2 = 0 + 3 -4t + t2 = 0 + 3 Combine like terms: 0 + 3 = 3 -4t + t2 = 3 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 + 4 Reorder the terms: 4 + -4t + t2 = 3 + 4 Combine like terms: 3 + 4 = 7 4 + -4t + t2 = 7 Factor a perfect square on the left side: (t + -2)(t + -2) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (t + -2) equal to 2.645751311 and -2.645751311.Subproblem 1
t + -2 = 2.645751311 Simplifying t + -2 = 2.645751311 Reorder the terms: -2 + t = 2.645751311 Solving -2 + t = 2.645751311 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 = 2.645751311 + 2 Combine like terms: -2 + 2 = 0 0 + t = 2.645751311 + 2 t = 2.645751311 + 2 Combine like terms: 2.645751311 + 2 = 4.645751311 t = 4.645751311 Simplifying t = 4.645751311Subproblem 2
t + -2 = -2.645751311 Simplifying t + -2 = -2.645751311 Reorder the terms: -2 + t = -2.645751311 Solving -2 + t = -2.645751311 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 = -2.645751311 + 2 Combine like terms: -2 + 2 = 0 0 + t = -2.645751311 + 2 t = -2.645751311 + 2 Combine like terms: -2.645751311 + 2 = -0.645751311 t = -0.645751311 Simplifying t = -0.645751311Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.645751311, -0.645751311}Solution
t = {4.645751311, -0.645751311}
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