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Simplifying 0 = -16t2 + 70t + 10 Reorder the terms: 0 = 10 + 70t + -16t2 Solving 0 = 10 + 70t + -16t2 Solving for variable 't'. Combine like terms: 0 + -10 = -10 -10 + -70t + 16t2 = 10 + 70t + -16t2 + -10 + -70t + 16t2 Reorder the terms: -10 + -70t + 16t2 = 10 + -10 + 70t + -70t + -16t2 + 16t2 Combine like terms: 10 + -10 = 0 -10 + -70t + 16t2 = 0 + 70t + -70t + -16t2 + 16t2 -10 + -70t + 16t2 = 70t + -70t + -16t2 + 16t2 Combine like terms: 70t + -70t = 0 -10 + -70t + 16t2 = 0 + -16t2 + 16t2 -10 + -70t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -10 + -70t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + -35t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + -35t + 8t2)' equal to zero and attempt to solve: Simplifying -5 + -35t + 8t2 = 0 Solving -5 + -35t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.625 + -4.375t + t2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + -4.375t + 0.625 + t2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + -4.375t + t2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + -4.375t + t2 = 0 + 0.625 -4.375t + t2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 -4.375t + t2 = 0.625 The t term is -4.375t. Take half its coefficient (-2.1875). Square it (4.78515625) and add it to both sides. Add '4.78515625' to each side of the equation. -4.375t + 4.78515625 + t2 = 0.625 + 4.78515625 Reorder the terms: 4.78515625 + -4.375t + t2 = 0.625 + 4.78515625 Combine like terms: 0.625 + 4.78515625 = 5.41015625 4.78515625 + -4.375t + t2 = 5.41015625 Factor a perfect square on the left side: (t + -2.1875)(t + -2.1875) = 5.41015625 Calculate the square root of the right side: 2.325974258 Break this problem into two subproblems by setting (t + -2.1875) equal to 2.325974258 and -2.325974258.Subproblem 1
t + -2.1875 = 2.325974258 Simplifying t + -2.1875 = 2.325974258 Reorder the terms: -2.1875 + t = 2.325974258 Solving -2.1875 + t = 2.325974258 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.1875' to each side of the equation. -2.1875 + 2.1875 + t = 2.325974258 + 2.1875 Combine like terms: -2.1875 + 2.1875 = 0.0000 0.0000 + t = 2.325974258 + 2.1875 t = 2.325974258 + 2.1875 Combine like terms: 2.325974258 + 2.1875 = 4.513474258 t = 4.513474258 Simplifying t = 4.513474258Subproblem 2
t + -2.1875 = -2.325974258 Simplifying t + -2.1875 = -2.325974258 Reorder the terms: -2.1875 + t = -2.325974258 Solving -2.1875 + t = -2.325974258 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.1875' to each side of the equation. -2.1875 + 2.1875 + t = -2.325974258 + 2.1875 Combine like terms: -2.1875 + 2.1875 = 0.0000 0.0000 + t = -2.325974258 + 2.1875 t = -2.325974258 + 2.1875 Combine like terms: -2.325974258 + 2.1875 = -0.138474258 t = -0.138474258 Simplifying t = -0.138474258Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.513474258, -0.138474258}Solution
t = {4.513474258, -0.138474258}
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