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Simplifying -16t2 + 96t + 4 = 0 Reorder the terms: 4 + 96t + -16t2 = 0 Solving 4 + 96t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4'. 4(1 + 24t + -4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(1 + 24t + -4t2)' equal to zero and attempt to solve: Simplifying 1 + 24t + -4t2 = 0 Solving 1 + 24t + -4t2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -0.25 + -6t + t2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -6t + 0.25 + t2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -6t + t2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -6t + t2 = 0 + 0.25 -6t + t2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -6t + t2 = 0.25 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 = 0.25 + 9 Reorder the terms: 9 + -6t + t2 = 0.25 + 9 Combine like terms: 0.25 + 9 = 9.25 9 + -6t + t2 = 9.25 Factor a perfect square on the left side: (t + -3)(t + -3) = 9.25 Calculate the square root of the right side: 3.041381265 Break this problem into two subproblems by setting (t + -3) equal to 3.041381265 and -3.041381265.Subproblem 1
t + -3 = 3.041381265 Simplifying t + -3 = 3.041381265 Reorder the terms: -3 + t = 3.041381265 Solving -3 + t = 3.041381265 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 = 3.041381265 + 3 Combine like terms: -3 + 3 = 0 0 + t = 3.041381265 + 3 t = 3.041381265 + 3 Combine like terms: 3.041381265 + 3 = 6.041381265 t = 6.041381265 Simplifying t = 6.041381265Subproblem 2
t + -3 = -3.041381265 Simplifying t + -3 = -3.041381265 Reorder the terms: -3 + t = -3.041381265 Solving -3 + t = -3.041381265 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 = -3.041381265 + 3 Combine like terms: -3 + 3 = 0 0 + t = -3.041381265 + 3 t = -3.041381265 + 3 Combine like terms: -3.041381265 + 3 = -0.041381265 t = -0.041381265 Simplifying t = -0.041381265Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.041381265, -0.041381265}Solution
t = {6.041381265, -0.041381265}
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