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Simplifying 16t2 + -96t + 5 = 0 Reorder the terms: 5 + -96t + 16t2 = 0 Solving 5 + -96t + 16t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.3125 + -6t + t2 = 0 Move the constant term to the right: Add '-0.3125' to each side of the equation. 0.3125 + -6t + -0.3125 + t2 = 0 + -0.3125 Reorder the terms: 0.3125 + -0.3125 + -6t + t2 = 0 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + -6t + t2 = 0 + -0.3125 -6t + t2 = 0 + -0.3125 Combine like terms: 0 + -0.3125 = -0.3125 -6t + t2 = -0.3125 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 = -0.3125 + 9 Reorder the terms: 9 + -6t + t2 = -0.3125 + 9 Combine like terms: -0.3125 + 9 = 8.6875 9 + -6t + t2 = 8.6875 Factor a perfect square on the left side: (t + -3)(t + -3) = 8.6875 Calculate the square root of the right side: 2.947456531 Break this problem into two subproblems by setting (t + -3) equal to 2.947456531 and -2.947456531.Subproblem 1
t + -3 = 2.947456531 Simplifying t + -3 = 2.947456531 Reorder the terms: -3 + t = 2.947456531 Solving -3 + t = 2.947456531 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 = 2.947456531 + 3 Combine like terms: -3 + 3 = 0 0 + t = 2.947456531 + 3 t = 2.947456531 + 3 Combine like terms: 2.947456531 + 3 = 5.947456531 t = 5.947456531 Simplifying t = 5.947456531Subproblem 2
t + -3 = -2.947456531 Simplifying t + -3 = -2.947456531 Reorder the terms: -3 + t = -2.947456531 Solving -3 + t = -2.947456531 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 = -2.947456531 + 3 Combine like terms: -3 + 3 = 0 0 + t = -2.947456531 + 3 t = -2.947456531 + 3 Combine like terms: -2.947456531 + 3 = 0.052543469 t = 0.052543469 Simplifying t = 0.052543469Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.947456531, 0.052543469}
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