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Simplifying -16t2 + 64t + 6 = 0 Reorder the terms: 6 + 64t + -16t2 = 0 Solving 6 + 64t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(3 + 32t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + 32t + -8t2)' equal to zero and attempt to solve: Simplifying 3 + 32t + -8t2 = 0 Solving 3 + 32t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -0.375 + -4t + t2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + -4t + 0.375 + t2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + -4t + t2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + -4t + t2 = 0 + 0.375 -4t + t2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 -4t + t2 = 0.375 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 = 0.375 + 4 Reorder the terms: 4 + -4t + t2 = 0.375 + 4 Combine like terms: 0.375 + 4 = 4.375 4 + -4t + t2 = 4.375 Factor a perfect square on the left side: (t + -2)(t + -2) = 4.375 Calculate the square root of the right side: 2.091650066 Break this problem into two subproblems by setting (t + -2) equal to 2.091650066 and -2.091650066.Subproblem 1
t + -2 = 2.091650066 Simplifying t + -2 = 2.091650066 Reorder the terms: -2 + t = 2.091650066 Solving -2 + t = 2.091650066 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 = 2.091650066 + 2 Combine like terms: -2 + 2 = 0 0 + t = 2.091650066 + 2 t = 2.091650066 + 2 Combine like terms: 2.091650066 + 2 = 4.091650066 t = 4.091650066 Simplifying t = 4.091650066Subproblem 2
t + -2 = -2.091650066 Simplifying t + -2 = -2.091650066 Reorder the terms: -2 + t = -2.091650066 Solving -2 + t = -2.091650066 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 = -2.091650066 + 2 Combine like terms: -2 + 2 = 0 0 + t = -2.091650066 + 2 t = -2.091650066 + 2 Combine like terms: -2.091650066 + 2 = -0.091650066 t = -0.091650066 Simplifying t = -0.091650066Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.091650066, -0.091650066}Solution
t = {4.091650066, -0.091650066}
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