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Simplifying -16t2 + 5t + 116 = 0 Reorder the terms: 116 + 5t + -16t2 = 0 Solving 116 + 5t + -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'. -7.25 + -0.3125t + t2 = 0 Move the constant term to the right: Add '7.25' to each side of the equation. -7.25 + -0.3125t + 7.25 + t2 = 0 + 7.25 Reorder the terms: -7.25 + 7.25 + -0.3125t + t2 = 0 + 7.25 Combine like terms: -7.25 + 7.25 = 0.00 0.00 + -0.3125t + t2 = 0 + 7.25 -0.3125t + t2 = 0 + 7.25 Combine like terms: 0 + 7.25 = 7.25 -0.3125t + t2 = 7.25 The t term is -0.3125t. Take half its coefficient (-0.15625). Square it (0.0244140625) and add it to both sides. Add '0.0244140625' to each side of the equation. -0.3125t + 0.0244140625 + t2 = 7.25 + 0.0244140625 Reorder the terms: 0.0244140625 + -0.3125t + t2 = 7.25 + 0.0244140625 Combine like terms: 7.25 + 0.0244140625 = 7.2744140625 0.0244140625 + -0.3125t + t2 = 7.2744140625 Factor a perfect square on the left side: (t + -0.15625)(t + -0.15625) = 7.2744140625 Calculate the square root of the right side: 2.697112171 Break this problem into two subproblems by setting (t + -0.15625) equal to 2.697112171 and -2.697112171.Subproblem 1
t + -0.15625 = 2.697112171 Simplifying t + -0.15625 = 2.697112171 Reorder the terms: -0.15625 + t = 2.697112171 Solving -0.15625 + t = 2.697112171 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.15625' to each side of the equation. -0.15625 + 0.15625 + t = 2.697112171 + 0.15625 Combine like terms: -0.15625 + 0.15625 = 0.00000 0.00000 + t = 2.697112171 + 0.15625 t = 2.697112171 + 0.15625 Combine like terms: 2.697112171 + 0.15625 = 2.853362171 t = 2.853362171 Simplifying t = 2.853362171Subproblem 2
t + -0.15625 = -2.697112171 Simplifying t + -0.15625 = -2.697112171 Reorder the terms: -0.15625 + t = -2.697112171 Solving -0.15625 + t = -2.697112171 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.15625' to each side of the equation. -0.15625 + 0.15625 + t = -2.697112171 + 0.15625 Combine like terms: -0.15625 + 0.15625 = 0.00000 0.00000 + t = -2.697112171 + 0.15625 t = -2.697112171 + 0.15625 Combine like terms: -2.697112171 + 0.15625 = -2.540862171 t = -2.540862171 Simplifying t = -2.540862171Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.853362171, -2.540862171}
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