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Simplifying 16t2 + 70t + 4 = 6 Reorder the terms: 4 + 70t + 16t2 = 6 Solving 4 + 70t + 16t2 = 6 Solving for variable 't'. Reorder the terms: 4 + -6 + 70t + 16t2 = 6 + -6 Combine like terms: 4 + -6 = -2 -2 + 70t + 16t2 = 6 + -6 Combine like terms: 6 + -6 = 0 -2 + 70t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + 35t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + 35t + 8t2)' equal to zero and attempt to solve: Simplifying -1 + 35t + 8t2 = 0 Solving -1 + 35t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.125 + 4.375t + t2 = 0 Move the constant term to the right: Add '0.125' to each side of the equation. -0.125 + 4.375t + 0.125 + t2 = 0 + 0.125 Reorder the terms: -0.125 + 0.125 + 4.375t + t2 = 0 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + 4.375t + t2 = 0 + 0.125 4.375t + t2 = 0 + 0.125 Combine like terms: 0 + 0.125 = 0.125 4.375t + t2 = 0.125 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 = 0.125 + 4.78515625 Reorder the terms: 4.78515625 + 4.375t + t2 = 0.125 + 4.78515625 Combine like terms: 0.125 + 4.78515625 = 4.91015625 4.78515625 + 4.375t + t2 = 4.91015625 Factor a perfect square on the left side: (t + 2.1875)(t + 2.1875) = 4.91015625 Calculate the square root of the right side: 2.215887238 Break this problem into two subproblems by setting (t + 2.1875) equal to 2.215887238 and -2.215887238.Subproblem 1
t + 2.1875 = 2.215887238 Simplifying t + 2.1875 = 2.215887238 Reorder the terms: 2.1875 + t = 2.215887238 Solving 2.1875 + t = 2.215887238 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 = 2.215887238 + -2.1875 Combine like terms: 2.1875 + -2.1875 = 0.0000 0.0000 + t = 2.215887238 + -2.1875 t = 2.215887238 + -2.1875 Combine like terms: 2.215887238 + -2.1875 = 0.028387238 t = 0.028387238 Simplifying t = 0.028387238Subproblem 2
t + 2.1875 = -2.215887238 Simplifying t + 2.1875 = -2.215887238 Reorder the terms: 2.1875 + t = -2.215887238 Solving 2.1875 + t = -2.215887238 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 = -2.215887238 + -2.1875 Combine like terms: 2.1875 + -2.1875 = 0.0000 0.0000 + t = -2.215887238 + -2.1875 t = -2.215887238 + -2.1875 Combine like terms: -2.215887238 + -2.1875 = -4.403387238 t = -4.403387238 Simplifying t = -4.403387238Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.028387238, -4.403387238}Solution
t = {0.028387238, -4.403387238}
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