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Simplifying -16t2 + 142t + 64 = 0 Reorder the terms: 64 + 142t + -16t2 = 0 Solving 64 + 142t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(32 + 71t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(32 + 71t + -8t2)' equal to zero and attempt to solve: Simplifying 32 + 71t + -8t2 = 0 Solving 32 + 71t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -4 + -8.875t + t2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -8.875t + 4 + t2 = 0 + 4 Reorder the terms: -4 + 4 + -8.875t + t2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -8.875t + t2 = 0 + 4 -8.875t + t2 = 0 + 4 Combine like terms: 0 + 4 = 4 -8.875t + t2 = 4 The t term is -8.875t. Take half its coefficient (-4.4375). Square it (19.69140625) and add it to both sides. Add '19.69140625' to each side of the equation. -8.875t + 19.69140625 + t2 = 4 + 19.69140625 Reorder the terms: 19.69140625 + -8.875t + t2 = 4 + 19.69140625 Combine like terms: 4 + 19.69140625 = 23.69140625 19.69140625 + -8.875t + t2 = 23.69140625 Factor a perfect square on the left side: (t + -4.4375)(t + -4.4375) = 23.69140625 Calculate the square root of the right side: 4.867381868 Break this problem into two subproblems by setting (t + -4.4375) equal to 4.867381868 and -4.867381868.Subproblem 1
t + -4.4375 = 4.867381868 Simplifying t + -4.4375 = 4.867381868 Reorder the terms: -4.4375 + t = 4.867381868 Solving -4.4375 + t = 4.867381868 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.4375' to each side of the equation. -4.4375 + 4.4375 + t = 4.867381868 + 4.4375 Combine like terms: -4.4375 + 4.4375 = 0.0000 0.0000 + t = 4.867381868 + 4.4375 t = 4.867381868 + 4.4375 Combine like terms: 4.867381868 + 4.4375 = 9.304881868 t = 9.304881868 Simplifying t = 9.304881868Subproblem 2
t + -4.4375 = -4.867381868 Simplifying t + -4.4375 = -4.867381868 Reorder the terms: -4.4375 + t = -4.867381868 Solving -4.4375 + t = -4.867381868 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.4375' to each side of the equation. -4.4375 + 4.4375 + t = -4.867381868 + 4.4375 Combine like terms: -4.4375 + 4.4375 = 0.0000 0.0000 + t = -4.867381868 + 4.4375 t = -4.867381868 + 4.4375 Combine like terms: -4.867381868 + 4.4375 = -0.429881868 t = -0.429881868 Simplifying t = -0.429881868Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.304881868, -0.429881868}Solution
t = {9.304881868, -0.429881868}
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