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Simplifying 0 = -16t2 + 5t + 15 Reorder the terms: 0 = 15 + 5t + -16t2 Solving 0 = 15 + 5t + -16t2 Solving for variable 't'. Combine like terms: 0 + -15 = -15 -15 + -5t + 16t2 = 15 + 5t + -16t2 + -15 + -5t + 16t2 Reorder the terms: -15 + -5t + 16t2 = 15 + -15 + 5t + -5t + -16t2 + 16t2 Combine like terms: 15 + -15 = 0 -15 + -5t + 16t2 = 0 + 5t + -5t + -16t2 + 16t2 -15 + -5t + 16t2 = 5t + -5t + -16t2 + 16t2 Combine like terms: 5t + -5t = 0 -15 + -5t + 16t2 = 0 + -16t2 + 16t2 -15 + -5t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -15 + -5t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.9375 + -0.3125t + t2 = 0 Move the constant term to the right: Add '0.9375' to each side of the equation. -0.9375 + -0.3125t + 0.9375 + t2 = 0 + 0.9375 Reorder the terms: -0.9375 + 0.9375 + -0.3125t + t2 = 0 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + -0.3125t + t2 = 0 + 0.9375 -0.3125t + t2 = 0 + 0.9375 Combine like terms: 0 + 0.9375 = 0.9375 -0.3125t + t2 = 0.9375 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 = 0.9375 + 0.0244140625 Reorder the terms: 0.0244140625 + -0.3125t + t2 = 0.9375 + 0.0244140625 Combine like terms: 0.9375 + 0.0244140625 = 0.9619140625 0.0244140625 + -0.3125t + t2 = 0.9619140625 Factor a perfect square on the left side: (t + -0.15625)(t + -0.15625) = 0.9619140625 Calculate the square root of the right side: 0.980772177 Break this problem into two subproblems by setting (t + -0.15625) equal to 0.980772177 and -0.980772177.Subproblem 1
t + -0.15625 = 0.980772177 Simplifying t + -0.15625 = 0.980772177 Reorder the terms: -0.15625 + t = 0.980772177 Solving -0.15625 + t = 0.980772177 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 = 0.980772177 + 0.15625 Combine like terms: -0.15625 + 0.15625 = 0.00000 0.00000 + t = 0.980772177 + 0.15625 t = 0.980772177 + 0.15625 Combine like terms: 0.980772177 + 0.15625 = 1.137022177 t = 1.137022177 Simplifying t = 1.137022177Subproblem 2
t + -0.15625 = -0.980772177 Simplifying t + -0.15625 = -0.980772177 Reorder the terms: -0.15625 + t = -0.980772177 Solving -0.15625 + t = -0.980772177 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 = -0.980772177 + 0.15625 Combine like terms: -0.15625 + 0.15625 = 0.00000 0.00000 + t = -0.980772177 + 0.15625 t = -0.980772177 + 0.15625 Combine like terms: -0.980772177 + 0.15625 = -0.824522177 t = -0.824522177 Simplifying t = -0.824522177Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.137022177, -0.824522177}
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