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Simplifying -16t2 + 192t + 9 = 0 Reorder the terms: 9 + 192t + -16t2 = 0 Solving 9 + 192t + -16t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -0.5625 + -12t + t2 = 0 Move the constant term to the right: Add '0.5625' to each side of the equation. -0.5625 + -12t + 0.5625 + t2 = 0 + 0.5625 Reorder the terms: -0.5625 + 0.5625 + -12t + t2 = 0 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + -12t + t2 = 0 + 0.5625 -12t + t2 = 0 + 0.5625 Combine like terms: 0 + 0.5625 = 0.5625 -12t + t2 = 0.5625 The t term is -12t. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12t + 36 + t2 = 0.5625 + 36 Reorder the terms: 36 + -12t + t2 = 0.5625 + 36 Combine like terms: 0.5625 + 36 = 36.5625 36 + -12t + t2 = 36.5625 Factor a perfect square on the left side: (t + -6)(t + -6) = 36.5625 Calculate the square root of the right side: 6.046693311 Break this problem into two subproblems by setting (t + -6) equal to 6.046693311 and -6.046693311.Subproblem 1
t + -6 = 6.046693311 Simplifying t + -6 = 6.046693311 Reorder the terms: -6 + t = 6.046693311 Solving -6 + t = 6.046693311 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + t = 6.046693311 + 6 Combine like terms: -6 + 6 = 0 0 + t = 6.046693311 + 6 t = 6.046693311 + 6 Combine like terms: 6.046693311 + 6 = 12.046693311 t = 12.046693311 Simplifying t = 12.046693311Subproblem 2
t + -6 = -6.046693311 Simplifying t + -6 = -6.046693311 Reorder the terms: -6 + t = -6.046693311 Solving -6 + t = -6.046693311 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + t = -6.046693311 + 6 Combine like terms: -6 + 6 = 0 0 + t = -6.046693311 + 6 t = -6.046693311 + 6 Combine like terms: -6.046693311 + 6 = -0.046693311 t = -0.046693311 Simplifying t = -0.046693311Solution
The solution to the problem is based on the solutions from the subproblems. t = {12.046693311, -0.046693311}
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