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Simplifying 0 = -16t2 + 14t + 6 Reorder the terms: 0 = 6 + 14t + -16t2 Solving 0 = 6 + 14t + -16t2 Solving for variable 't'. Combine like terms: 0 + -6 = -6 -6 + -14t + 16t2 = 6 + 14t + -16t2 + -6 + -14t + 16t2 Reorder the terms: -6 + -14t + 16t2 = 6 + -6 + 14t + -14t + -16t2 + 16t2 Combine like terms: 6 + -6 = 0 -6 + -14t + 16t2 = 0 + 14t + -14t + -16t2 + 16t2 -6 + -14t + 16t2 = 14t + -14t + -16t2 + 16t2 Combine like terms: 14t + -14t = 0 -6 + -14t + 16t2 = 0 + -16t2 + 16t2 -6 + -14t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -6 + -14t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + -7t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + -7t + 8t2)' equal to zero and attempt to solve: Simplifying -3 + -7t + 8t2 = 0 Solving -3 + -7t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.375 + -0.875t + t2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + -0.875t + 0.375 + t2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + -0.875t + t2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + -0.875t + t2 = 0 + 0.375 -0.875t + t2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 -0.875t + t2 = 0.375 The t term is -0.875t. Take half its coefficient (-0.4375). Square it (0.19140625) and add it to both sides. Add '0.19140625' to each side of the equation. -0.875t + 0.19140625 + t2 = 0.375 + 0.19140625 Reorder the terms: 0.19140625 + -0.875t + t2 = 0.375 + 0.19140625 Combine like terms: 0.375 + 0.19140625 = 0.56640625 0.19140625 + -0.875t + t2 = 0.56640625 Factor a perfect square on the left side: (t + -0.4375)(t + -0.4375) = 0.56640625 Calculate the square root of the right side: 0.752599661 Break this problem into two subproblems by setting (t + -0.4375) equal to 0.752599661 and -0.752599661.Subproblem 1
t + -0.4375 = 0.752599661 Simplifying t + -0.4375 = 0.752599661 Reorder the terms: -0.4375 + t = 0.752599661 Solving -0.4375 + t = 0.752599661 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.4375' to each side of the equation. -0.4375 + 0.4375 + t = 0.752599661 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + t = 0.752599661 + 0.4375 t = 0.752599661 + 0.4375 Combine like terms: 0.752599661 + 0.4375 = 1.190099661 t = 1.190099661 Simplifying t = 1.190099661Subproblem 2
t + -0.4375 = -0.752599661 Simplifying t + -0.4375 = -0.752599661 Reorder the terms: -0.4375 + t = -0.752599661 Solving -0.4375 + t = -0.752599661 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.4375' to each side of the equation. -0.4375 + 0.4375 + t = -0.752599661 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + t = -0.752599661 + 0.4375 t = -0.752599661 + 0.4375 Combine like terms: -0.752599661 + 0.4375 = -0.315099661 t = -0.315099661 Simplifying t = -0.315099661Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.190099661, -0.315099661}Solution
t = {1.190099661, -0.315099661}
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