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Simplifying -16t2 + 34t + 336 = 0 Reorder the terms: 336 + 34t + -16t2 = 0 Solving 336 + 34t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(168 + 17t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(168 + 17t + -8t2)' equal to zero and attempt to solve: Simplifying 168 + 17t + -8t2 = 0 Solving 168 + 17t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -21 + -2.125t + t2 = 0 Move the constant term to the right: Add '21' to each side of the equation. -21 + -2.125t + 21 + t2 = 0 + 21 Reorder the terms: -21 + 21 + -2.125t + t2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + -2.125t + t2 = 0 + 21 -2.125t + t2 = 0 + 21 Combine like terms: 0 + 21 = 21 -2.125t + t2 = 21 The t term is -2.125t. Take half its coefficient (-1.0625). Square it (1.12890625) and add it to both sides. Add '1.12890625' to each side of the equation. -2.125t + 1.12890625 + t2 = 21 + 1.12890625 Reorder the terms: 1.12890625 + -2.125t + t2 = 21 + 1.12890625 Combine like terms: 21 + 1.12890625 = 22.12890625 1.12890625 + -2.125t + t2 = 22.12890625 Factor a perfect square on the left side: (t + -1.0625)(t + -1.0625) = 22.12890625 Calculate the square root of the right side: 4.704137142 Break this problem into two subproblems by setting (t + -1.0625) equal to 4.704137142 and -4.704137142.Subproblem 1
t + -1.0625 = 4.704137142 Simplifying t + -1.0625 = 4.704137142 Reorder the terms: -1.0625 + t = 4.704137142 Solving -1.0625 + t = 4.704137142 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.0625' to each side of the equation. -1.0625 + 1.0625 + t = 4.704137142 + 1.0625 Combine like terms: -1.0625 + 1.0625 = 0.0000 0.0000 + t = 4.704137142 + 1.0625 t = 4.704137142 + 1.0625 Combine like terms: 4.704137142 + 1.0625 = 5.766637142 t = 5.766637142 Simplifying t = 5.766637142Subproblem 2
t + -1.0625 = -4.704137142 Simplifying t + -1.0625 = -4.704137142 Reorder the terms: -1.0625 + t = -4.704137142 Solving -1.0625 + t = -4.704137142 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.0625' to each side of the equation. -1.0625 + 1.0625 + t = -4.704137142 + 1.0625 Combine like terms: -1.0625 + 1.0625 = 0.0000 0.0000 + t = -4.704137142 + 1.0625 t = -4.704137142 + 1.0625 Combine like terms: -4.704137142 + 1.0625 = -3.641637142 t = -3.641637142 Simplifying t = -3.641637142Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.766637142, -3.641637142}Solution
t = {5.766637142, -3.641637142}
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