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Simplifying -16t2 + 96t + 8 = 0 Reorder the terms: 8 + 96t + -16t2 = 0 Solving 8 + 96t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '8'. 8(1 + 12t + -2t2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(1 + 12t + -2t2)' equal to zero and attempt to solve: Simplifying 1 + 12t + -2t2 = 0 Solving 1 + 12t + -2t2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -0.5 + -6t + t2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -6t + 0.5 + t2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -6t + t2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -6t + t2 = 0 + 0.5 -6t + t2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -6t + t2 = 0.5 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 = 0.5 + 9 Reorder the terms: 9 + -6t + t2 = 0.5 + 9 Combine like terms: 0.5 + 9 = 9.5 9 + -6t + t2 = 9.5 Factor a perfect square on the left side: (t + -3)(t + -3) = 9.5 Calculate the square root of the right side: 3.082207001 Break this problem into two subproblems by setting (t + -3) equal to 3.082207001 and -3.082207001.Subproblem 1
t + -3 = 3.082207001 Simplifying t + -3 = 3.082207001 Reorder the terms: -3 + t = 3.082207001 Solving -3 + t = 3.082207001 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 = 3.082207001 + 3 Combine like terms: -3 + 3 = 0 0 + t = 3.082207001 + 3 t = 3.082207001 + 3 Combine like terms: 3.082207001 + 3 = 6.082207001 t = 6.082207001 Simplifying t = 6.082207001Subproblem 2
t + -3 = -3.082207001 Simplifying t + -3 = -3.082207001 Reorder the terms: -3 + t = -3.082207001 Solving -3 + t = -3.082207001 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 = -3.082207001 + 3 Combine like terms: -3 + 3 = 0 0 + t = -3.082207001 + 3 t = -3.082207001 + 3 Combine like terms: -3.082207001 + 3 = -0.082207001 t = -0.082207001 Simplifying t = -0.082207001Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.082207001, -0.082207001}Solution
t = {6.082207001, -0.082207001}
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