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Simplifying 16t2 + 416t + -768 = 0 Reorder the terms: -768 + 416t + 16t2 = 0 Solving -768 + 416t + 16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '16'. 16(-48 + 26t + t2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(-48 + 26t + t2)' equal to zero and attempt to solve: Simplifying -48 + 26t + t2 = 0 Solving -48 + 26t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '48' to each side of the equation. -48 + 26t + 48 + t2 = 0 + 48 Reorder the terms: -48 + 48 + 26t + t2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + 26t + t2 = 0 + 48 26t + t2 = 0 + 48 Combine like terms: 0 + 48 = 48 26t + t2 = 48 The t term is 26t. Take half its coefficient (13). Square it (169) and add it to both sides. Add '169' to each side of the equation. 26t + 169 + t2 = 48 + 169 Reorder the terms: 169 + 26t + t2 = 48 + 169 Combine like terms: 48 + 169 = 217 169 + 26t + t2 = 217 Factor a perfect square on the left side: (t + 13)(t + 13) = 217 Calculate the square root of the right side: 14.730919863 Break this problem into two subproblems by setting (t + 13) equal to 14.730919863 and -14.730919863.Subproblem 1
t + 13 = 14.730919863 Simplifying t + 13 = 14.730919863 Reorder the terms: 13 + t = 14.730919863 Solving 13 + t = 14.730919863 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + t = 14.730919863 + -13 Combine like terms: 13 + -13 = 0 0 + t = 14.730919863 + -13 t = 14.730919863 + -13 Combine like terms: 14.730919863 + -13 = 1.730919863 t = 1.730919863 Simplifying t = 1.730919863Subproblem 2
t + 13 = -14.730919863 Simplifying t + 13 = -14.730919863 Reorder the terms: 13 + t = -14.730919863 Solving 13 + t = -14.730919863 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + t = -14.730919863 + -13 Combine like terms: 13 + -13 = 0 0 + t = -14.730919863 + -13 t = -14.730919863 + -13 Combine like terms: -14.730919863 + -13 = -27.730919863 t = -27.730919863 Simplifying t = -27.730919863Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.730919863, -27.730919863}Solution
t = {1.730919863, -27.730919863}
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