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Simplifying 70 = 16t2 + 128t Reorder the terms: 70 = 128t + 16t2 Solving 70 = 128t + 16t2 Solving for variable 't'. Reorder the terms: 70 + -128t + -16t2 = 128t + -128t + 16t2 + -16t2 Combine like terms: 128t + -128t = 0 70 + -128t + -16t2 = 0 + 16t2 + -16t2 70 + -128t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 70 + -128t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(35 + -64t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(35 + -64t + -8t2)' equal to zero and attempt to solve: Simplifying 35 + -64t + -8t2 = 0 Solving 35 + -64t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -4.375 + 8t + t2 = 0 Move the constant term to the right: Add '4.375' to each side of the equation. -4.375 + 8t + 4.375 + t2 = 0 + 4.375 Reorder the terms: -4.375 + 4.375 + 8t + t2 = 0 + 4.375 Combine like terms: -4.375 + 4.375 = 0.000 0.000 + 8t + t2 = 0 + 4.375 8t + t2 = 0 + 4.375 Combine like terms: 0 + 4.375 = 4.375 8t + t2 = 4.375 The t term is 8t. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8t + 16 + t2 = 4.375 + 16 Reorder the terms: 16 + 8t + t2 = 4.375 + 16 Combine like terms: 4.375 + 16 = 20.375 16 + 8t + t2 = 20.375 Factor a perfect square on the left side: (t + 4)(t + 4) = 20.375 Calculate the square root of the right side: 4.513867521 Break this problem into two subproblems by setting (t + 4) equal to 4.513867521 and -4.513867521.Subproblem 1
t + 4 = 4.513867521 Simplifying t + 4 = 4.513867521 Reorder the terms: 4 + t = 4.513867521 Solving 4 + t = 4.513867521 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + t = 4.513867521 + -4 Combine like terms: 4 + -4 = 0 0 + t = 4.513867521 + -4 t = 4.513867521 + -4 Combine like terms: 4.513867521 + -4 = 0.513867521 t = 0.513867521 Simplifying t = 0.513867521Subproblem 2
t + 4 = -4.513867521 Simplifying t + 4 = -4.513867521 Reorder the terms: 4 + t = -4.513867521 Solving 4 + t = -4.513867521 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + t = -4.513867521 + -4 Combine like terms: 4 + -4 = 0 0 + t = -4.513867521 + -4 t = -4.513867521 + -4 Combine like terms: -4.513867521 + -4 = -8.513867521 t = -8.513867521 Simplifying t = -8.513867521Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.513867521, -8.513867521}Solution
t = {0.513867521, -8.513867521}
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