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Simplifying 0 = (-16t2) + 64t + 656 Reorder the terms: 0 = 656 + 64t + (-16t2) Solving 0 = 656 + 64t + (-16t2) Solving for variable 't'. Combine like terms: 0 + -656 = -656 -656 + -64t + (16t2) = 656 + 64t + (-16t2) + -656 + -64t + (16t2) Reorder the terms: -656 + -64t + (16t2) = 656 + -656 + 64t + -64t + (-16t2) + (16t2) Combine like terms: 656 + -656 = 0 -656 + -64t + (16t2) = 0 + 64t + -64t + (-16t2) + (16t2) -656 + -64t + (16t2) = 64t + -64t + (-16t2) + (16t2) Combine like terms: 64t + -64t = 0 -656 + -64t + (16t2) = 0 + (-16t2) + (16t2) -656 + -64t + (16t2) = (-16t2) + (16t2) Combine like terms: (-16t2) + (16t2) = 0 -656 + -64t + (16t2) = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(-41 + -4t + t2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(-41 + -4t + t2)' equal to zero and attempt to solve: Simplifying -41 + -4t + t2 = 0 Solving -41 + -4t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '41' to each side of the equation. -41 + -4t + 41 + t2 = 0 + 41 Reorder the terms: -41 + 41 + -4t + t2 = 0 + 41 Combine like terms: -41 + 41 = 0 0 + -4t + t2 = 0 + 41 -4t + t2 = 0 + 41 Combine like terms: 0 + 41 = 41 -4t + t2 = 41 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 = 41 + 4 Reorder the terms: 4 + -4t + t2 = 41 + 4 Combine like terms: 41 + 4 = 45 4 + -4t + t2 = 45 Factor a perfect square on the left side: (t + -2)(t + -2) = 45 Calculate the square root of the right side: 6.708203933 Break this problem into two subproblems by setting (t + -2) equal to 6.708203933 and -6.708203933.Subproblem 1
t + -2 = 6.708203933 Simplifying t + -2 = 6.708203933 Reorder the terms: -2 + t = 6.708203933 Solving -2 + t = 6.708203933 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 = 6.708203933 + 2 Combine like terms: -2 + 2 = 0 0 + t = 6.708203933 + 2 t = 6.708203933 + 2 Combine like terms: 6.708203933 + 2 = 8.708203933 t = 8.708203933 Simplifying t = 8.708203933Subproblem 2
t + -2 = -6.708203933 Simplifying t + -2 = -6.708203933 Reorder the terms: -2 + t = -6.708203933 Solving -2 + t = -6.708203933 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 = -6.708203933 + 2 Combine like terms: -2 + 2 = 0 0 + t = -6.708203933 + 2 t = -6.708203933 + 2 Combine like terms: -6.708203933 + 2 = -4.708203933 t = -4.708203933 Simplifying t = -4.708203933Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.708203933, -4.708203933}Solution
t = {8.708203933, -4.708203933}
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