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Simplifying -16t2 + 64t + -1 = 0 Reorder the terms: -1 + 64t + -16t2 = 0 Solving -1 + 64t + -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'. 0.0625 + -4t + t2 = 0 Move the constant term to the right: Add '-0.0625' to each side of the equation. 0.0625 + -4t + -0.0625 + t2 = 0 + -0.0625 Reorder the terms: 0.0625 + -0.0625 + -4t + t2 = 0 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + -4t + t2 = 0 + -0.0625 -4t + t2 = 0 + -0.0625 Combine like terms: 0 + -0.0625 = -0.0625 -4t + t2 = -0.0625 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 = -0.0625 + 4 Reorder the terms: 4 + -4t + t2 = -0.0625 + 4 Combine like terms: -0.0625 + 4 = 3.9375 4 + -4t + t2 = 3.9375 Factor a perfect square on the left side: (t + -2)(t + -2) = 3.9375 Calculate the square root of the right side: 1.984313483 Break this problem into two subproblems by setting (t + -2) equal to 1.984313483 and -1.984313483.Subproblem 1
t + -2 = 1.984313483 Simplifying t + -2 = 1.984313483 Reorder the terms: -2 + t = 1.984313483 Solving -2 + t = 1.984313483 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 = 1.984313483 + 2 Combine like terms: -2 + 2 = 0 0 + t = 1.984313483 + 2 t = 1.984313483 + 2 Combine like terms: 1.984313483 + 2 = 3.984313483 t = 3.984313483 Simplifying t = 3.984313483Subproblem 2
t + -2 = -1.984313483 Simplifying t + -2 = -1.984313483 Reorder the terms: -2 + t = -1.984313483 Solving -2 + t = -1.984313483 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 = -1.984313483 + 2 Combine like terms: -2 + 2 = 0 0 + t = -1.984313483 + 2 t = -1.984313483 + 2 Combine like terms: -1.984313483 + 2 = 0.015686517 t = 0.015686517 Simplifying t = 0.015686517Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.984313483, 0.015686517}
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