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Simplifying (38t + -16t2) + -16 = 0 Remove parenthesis around (38t + -16t2) 38t + -16t2 + -16 = 0 Reorder the terms: -16 + 38t + -16t2 = 0 Solving -16 + 38t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(-8 + 19t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-8 + 19t + -8t2)' equal to zero and attempt to solve: Simplifying -8 + 19t + -8t2 = 0 Solving -8 + 19t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. 1 + -2.375t + t2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -2.375t + -1 + t2 = 0 + -1 Reorder the terms: 1 + -1 + -2.375t + t2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2.375t + t2 = 0 + -1 -2.375t + t2 = 0 + -1 Combine like terms: 0 + -1 = -1 -2.375t + t2 = -1 The t term is -2.375t. Take half its coefficient (-1.1875). Square it (1.41015625) and add it to both sides. Add '1.41015625' to each side of the equation. -2.375t + 1.41015625 + t2 = -1 + 1.41015625 Reorder the terms: 1.41015625 + -2.375t + t2 = -1 + 1.41015625 Combine like terms: -1 + 1.41015625 = 0.41015625 1.41015625 + -2.375t + t2 = 0.41015625 Factor a perfect square on the left side: (t + -1.1875)(t + -1.1875) = 0.41015625 Calculate the square root of the right side: 0.640434423 Break this problem into two subproblems by setting (t + -1.1875) equal to 0.640434423 and -0.640434423.Subproblem 1
t + -1.1875 = 0.640434423 Simplifying t + -1.1875 = 0.640434423 Reorder the terms: -1.1875 + t = 0.640434423 Solving -1.1875 + t = 0.640434423 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.1875' to each side of the equation. -1.1875 + 1.1875 + t = 0.640434423 + 1.1875 Combine like terms: -1.1875 + 1.1875 = 0.0000 0.0000 + t = 0.640434423 + 1.1875 t = 0.640434423 + 1.1875 Combine like terms: 0.640434423 + 1.1875 = 1.827934423 t = 1.827934423 Simplifying t = 1.827934423Subproblem 2
t + -1.1875 = -0.640434423 Simplifying t + -1.1875 = -0.640434423 Reorder the terms: -1.1875 + t = -0.640434423 Solving -1.1875 + t = -0.640434423 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.1875' to each side of the equation. -1.1875 + 1.1875 + t = -0.640434423 + 1.1875 Combine like terms: -1.1875 + 1.1875 = 0.0000 0.0000 + t = -0.640434423 + 1.1875 t = -0.640434423 + 1.1875 Combine like terms: -0.640434423 + 1.1875 = 0.547065577 t = 0.547065577 Simplifying t = 0.547065577Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.827934423, 0.547065577}Solution
t = {1.827934423, 0.547065577}
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