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Simplifying -16t2 + 38t + -14 = 0 Reorder the terms: -14 + 38t + -16t2 = 0 Solving -14 + 38t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(-7 + 19t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-7 + 19t + -8t2)' equal to zero and attempt to solve: Simplifying -7 + 19t + -8t2 = 0 Solving -7 + 19t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. 0.875 + -2.375t + t2 = 0 Move the constant term to the right: Add '-0.875' to each side of the equation. 0.875 + -2.375t + -0.875 + t2 = 0 + -0.875 Reorder the terms: 0.875 + -0.875 + -2.375t + t2 = 0 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + -2.375t + t2 = 0 + -0.875 -2.375t + t2 = 0 + -0.875 Combine like terms: 0 + -0.875 = -0.875 -2.375t + t2 = -0.875 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 = -0.875 + 1.41015625 Reorder the terms: 1.41015625 + -2.375t + t2 = -0.875 + 1.41015625 Combine like terms: -0.875 + 1.41015625 = 0.53515625 1.41015625 + -2.375t + t2 = 0.53515625 Factor a perfect square on the left side: (t + -1.1875)(t + -1.1875) = 0.53515625 Calculate the square root of the right side: 0.731543744 Break this problem into two subproblems by setting (t + -1.1875) equal to 0.731543744 and -0.731543744.Subproblem 1
t + -1.1875 = 0.731543744 Simplifying t + -1.1875 = 0.731543744 Reorder the terms: -1.1875 + t = 0.731543744 Solving -1.1875 + t = 0.731543744 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 = 0.731543744 + 1.1875 Combine like terms: -1.1875 + 1.1875 = 0.0000 0.0000 + t = 0.731543744 + 1.1875 t = 0.731543744 + 1.1875 Combine like terms: 0.731543744 + 1.1875 = 1.919043744 t = 1.919043744 Simplifying t = 1.919043744Subproblem 2
t + -1.1875 = -0.731543744 Simplifying t + -1.1875 = -0.731543744 Reorder the terms: -1.1875 + t = -0.731543744 Solving -1.1875 + t = -0.731543744 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 = -0.731543744 + 1.1875 Combine like terms: -1.1875 + 1.1875 = 0.0000 0.0000 + t = -0.731543744 + 1.1875 t = -0.731543744 + 1.1875 Combine like terms: -0.731543744 + 1.1875 = 0.455956256 t = 0.455956256 Simplifying t = 0.455956256Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.919043744, 0.455956256}Solution
t = {1.919043744, 0.455956256}
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