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Simplifying -16t2 + 26t + 96 = 0 Reorder the terms: 96 + 26t + -16t2 = 0 Solving 96 + 26t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(48 + 13t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(48 + 13t + -8t2)' equal to zero and attempt to solve: Simplifying 48 + 13t + -8t2 = 0 Solving 48 + 13t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -6 + -1.625t + t2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -1.625t + 6 + t2 = 0 + 6 Reorder the terms: -6 + 6 + -1.625t + t2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1.625t + t2 = 0 + 6 -1.625t + t2 = 0 + 6 Combine like terms: 0 + 6 = 6 -1.625t + t2 = 6 The t term is -1.625t. Take half its coefficient (-0.8125). Square it (0.66015625) and add it to both sides. Add '0.66015625' to each side of the equation. -1.625t + 0.66015625 + t2 = 6 + 0.66015625 Reorder the terms: 0.66015625 + -1.625t + t2 = 6 + 0.66015625 Combine like terms: 6 + 0.66015625 = 6.66015625 0.66015625 + -1.625t + t2 = 6.66015625 Factor a perfect square on the left side: (t + -0.8125)(t + -0.8125) = 6.66015625 Calculate the square root of the right side: 2.580727853 Break this problem into two subproblems by setting (t + -0.8125) equal to 2.580727853 and -2.580727853.Subproblem 1
t + -0.8125 = 2.580727853 Simplifying t + -0.8125 = 2.580727853 Reorder the terms: -0.8125 + t = 2.580727853 Solving -0.8125 + t = 2.580727853 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.8125' to each side of the equation. -0.8125 + 0.8125 + t = 2.580727853 + 0.8125 Combine like terms: -0.8125 + 0.8125 = 0.0000 0.0000 + t = 2.580727853 + 0.8125 t = 2.580727853 + 0.8125 Combine like terms: 2.580727853 + 0.8125 = 3.393227853 t = 3.393227853 Simplifying t = 3.393227853Subproblem 2
t + -0.8125 = -2.580727853 Simplifying t + -0.8125 = -2.580727853 Reorder the terms: -0.8125 + t = -2.580727853 Solving -0.8125 + t = -2.580727853 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.8125' to each side of the equation. -0.8125 + 0.8125 + t = -2.580727853 + 0.8125 Combine like terms: -0.8125 + 0.8125 = 0.0000 0.0000 + t = -2.580727853 + 0.8125 t = -2.580727853 + 0.8125 Combine like terms: -2.580727853 + 0.8125 = -1.768227853 t = -1.768227853 Simplifying t = -1.768227853Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.393227853, -1.768227853}Solution
t = {3.393227853, -1.768227853}
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