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Simplifying 4 = 70 + -4t + -16t2 Solving 4 = 70 + -4t + -16t2 Solving for variable 't'. Combine like terms: 4 + -70 = -66 -66 + 4t + 16t2 = 70 + -4t + -16t2 + -70 + 4t + 16t2 Reorder the terms: -66 + 4t + 16t2 = 70 + -70 + -4t + 4t + -16t2 + 16t2 Combine like terms: 70 + -70 = 0 -66 + 4t + 16t2 = 0 + -4t + 4t + -16t2 + 16t2 -66 + 4t + 16t2 = -4t + 4t + -16t2 + 16t2 Combine like terms: -4t + 4t = 0 -66 + 4t + 16t2 = 0 + -16t2 + 16t2 -66 + 4t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -66 + 4t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-33 + 2t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-33 + 2t + 8t2)' equal to zero and attempt to solve: Simplifying -33 + 2t + 8t2 = 0 Solving -33 + 2t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -4.125 + 0.25t + t2 = 0 Move the constant term to the right: Add '4.125' to each side of the equation. -4.125 + 0.25t + 4.125 + t2 = 0 + 4.125 Reorder the terms: -4.125 + 4.125 + 0.25t + t2 = 0 + 4.125 Combine like terms: -4.125 + 4.125 = 0.000 0.000 + 0.25t + t2 = 0 + 4.125 0.25t + t2 = 0 + 4.125 Combine like terms: 0 + 4.125 = 4.125 0.25t + t2 = 4.125 The t term is 0.25t. Take half its coefficient (0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. 0.25t + 0.015625 + t2 = 4.125 + 0.015625 Reorder the terms: 0.015625 + 0.25t + t2 = 4.125 + 0.015625 Combine like terms: 4.125 + 0.015625 = 4.140625 0.015625 + 0.25t + t2 = 4.140625 Factor a perfect square on the left side: (t + 0.125)(t + 0.125) = 4.140625 Calculate the square root of the right side: 2.034852575 Break this problem into two subproblems by setting (t + 0.125) equal to 2.034852575 and -2.034852575.Subproblem 1
t + 0.125 = 2.034852575 Simplifying t + 0.125 = 2.034852575 Reorder the terms: 0.125 + t = 2.034852575 Solving 0.125 + t = 2.034852575 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + t = 2.034852575 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + t = 2.034852575 + -0.125 t = 2.034852575 + -0.125 Combine like terms: 2.034852575 + -0.125 = 1.909852575 t = 1.909852575 Simplifying t = 1.909852575Subproblem 2
t + 0.125 = -2.034852575 Simplifying t + 0.125 = -2.034852575 Reorder the terms: 0.125 + t = -2.034852575 Solving 0.125 + t = -2.034852575 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + t = -2.034852575 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + t = -2.034852575 + -0.125 t = -2.034852575 + -0.125 Combine like terms: -2.034852575 + -0.125 = -2.159852575 t = -2.159852575 Simplifying t = -2.159852575Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.909852575, -2.159852575}Solution
t = {1.909852575, -2.159852575}
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