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Simplifying 0 = 16t2 + 14t + -14 Reorder the terms: 0 = -14 + 14t + 16t2 Solving 0 = -14 + 14t + 16t2 Solving for variable 't'. Combine like terms: 0 + 14 = 14 14 + -14t + -16t2 = -14 + 14t + 16t2 + 14 + -14t + -16t2 Reorder the terms: 14 + -14t + -16t2 = -14 + 14 + 14t + -14t + 16t2 + -16t2 Combine like terms: -14 + 14 = 0 14 + -14t + -16t2 = 0 + 14t + -14t + 16t2 + -16t2 14 + -14t + -16t2 = 14t + -14t + 16t2 + -16t2 Combine like terms: 14t + -14t = 0 14 + -14t + -16t2 = 0 + 16t2 + -16t2 14 + -14t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 14 + -14t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(7 + -7t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + -7t + -8t2)' equal to zero and attempt to solve: Simplifying 7 + -7t + -8t2 = 0 Solving 7 + -7t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -0.875 + 0.875t + t2 = 0 Move the constant term to the right: Add '0.875' to each side of the equation. -0.875 + 0.875t + 0.875 + t2 = 0 + 0.875 Reorder the terms: -0.875 + 0.875 + 0.875t + t2 = 0 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + 0.875t + t2 = 0 + 0.875 0.875t + t2 = 0 + 0.875 Combine like terms: 0 + 0.875 = 0.875 0.875t + t2 = 0.875 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 = 0.875 + 0.19140625 Reorder the terms: 0.19140625 + 0.875t + t2 = 0.875 + 0.19140625 Combine like terms: 0.875 + 0.19140625 = 1.06640625 0.19140625 + 0.875t + t2 = 1.06640625 Factor a perfect square on the left side: (t + 0.4375)(t + 0.4375) = 1.06640625 Calculate the square root of the right side: 1.032669478 Break this problem into two subproblems by setting (t + 0.4375) equal to 1.032669478 and -1.032669478.Subproblem 1
t + 0.4375 = 1.032669478 Simplifying t + 0.4375 = 1.032669478 Reorder the terms: 0.4375 + t = 1.032669478 Solving 0.4375 + t = 1.032669478 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 = 1.032669478 + -0.4375 Combine like terms: 0.4375 + -0.4375 = 0.0000 0.0000 + t = 1.032669478 + -0.4375 t = 1.032669478 + -0.4375 Combine like terms: 1.032669478 + -0.4375 = 0.595169478 t = 0.595169478 Simplifying t = 0.595169478Subproblem 2
t + 0.4375 = -1.032669478 Simplifying t + 0.4375 = -1.032669478 Reorder the terms: 0.4375 + t = -1.032669478 Solving 0.4375 + t = -1.032669478 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 = -1.032669478 + -0.4375 Combine like terms: 0.4375 + -0.4375 = 0.0000 0.0000 + t = -1.032669478 + -0.4375 t = -1.032669478 + -0.4375 Combine like terms: -1.032669478 + -0.4375 = -1.470169478 t = -1.470169478 Simplifying t = -1.470169478Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.595169478, -1.470169478}Solution
t = {0.595169478, -1.470169478}
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