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Simplifying -16t2 + 70t + 12 = 0 Reorder the terms: 12 + 70t + -16t2 = 0 Solving 12 + 70t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(6 + 35t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(6 + 35t + -8t2)' equal to zero and attempt to solve: Simplifying 6 + 35t + -8t2 = 0 Solving 6 + 35t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -0.75 + -4.375t + t2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + -4.375t + 0.75 + t2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + -4.375t + t2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + -4.375t + t2 = 0 + 0.75 -4.375t + t2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 -4.375t + t2 = 0.75 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 = 0.75 + 4.78515625 Reorder the terms: 4.78515625 + -4.375t + t2 = 0.75 + 4.78515625 Combine like terms: 0.75 + 4.78515625 = 5.53515625 4.78515625 + -4.375t + t2 = 5.53515625 Factor a perfect square on the left side: (t + -2.1875)(t + -2.1875) = 5.53515625 Calculate the square root of the right side: 2.352691278 Break this problem into two subproblems by setting (t + -2.1875) equal to 2.352691278 and -2.352691278.Subproblem 1
t + -2.1875 = 2.352691278 Simplifying t + -2.1875 = 2.352691278 Reorder the terms: -2.1875 + t = 2.352691278 Solving -2.1875 + t = 2.352691278 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 = 2.352691278 + 2.1875 Combine like terms: -2.1875 + 2.1875 = 0.0000 0.0000 + t = 2.352691278 + 2.1875 t = 2.352691278 + 2.1875 Combine like terms: 2.352691278 + 2.1875 = 4.540191278 t = 4.540191278 Simplifying t = 4.540191278Subproblem 2
t + -2.1875 = -2.352691278 Simplifying t + -2.1875 = -2.352691278 Reorder the terms: -2.1875 + t = -2.352691278 Solving -2.1875 + t = -2.352691278 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 = -2.352691278 + 2.1875 Combine like terms: -2.1875 + 2.1875 = 0.0000 0.0000 + t = -2.352691278 + 2.1875 t = -2.352691278 + 2.1875 Combine like terms: -2.352691278 + 2.1875 = -0.165191278 t = -0.165191278 Simplifying t = -0.165191278Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.540191278, -0.165191278}Solution
t = {4.540191278, -0.165191278}
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