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Simplifying 16t2 = 24t + 15 Reorder the terms: 16t2 = 15 + 24t Solving 16t2 = 15 + 24t Solving for variable 't'. Reorder the terms: -15 + -24t + 16t2 = 15 + 24t + -15 + -24t Reorder the terms: -15 + -24t + 16t2 = 15 + -15 + 24t + -24t Combine like terms: 15 + -15 = 0 -15 + -24t + 16t2 = 0 + 24t + -24t -15 + -24t + 16t2 = 24t + -24t Combine like terms: 24t + -24t = 0 -15 + -24t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.9375 + -1.5t + t2 = 0 Move the constant term to the right: Add '0.9375' to each side of the equation. -0.9375 + -1.5t + 0.9375 + t2 = 0 + 0.9375 Reorder the terms: -0.9375 + 0.9375 + -1.5t + t2 = 0 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + -1.5t + t2 = 0 + 0.9375 -1.5t + t2 = 0 + 0.9375 Combine like terms: 0 + 0.9375 = 0.9375 -1.5t + t2 = 0.9375 The t term is -1.5t. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5t + 0.5625 + t2 = 0.9375 + 0.5625 Reorder the terms: 0.5625 + -1.5t + t2 = 0.9375 + 0.5625 Combine like terms: 0.9375 + 0.5625 = 1.5 0.5625 + -1.5t + t2 = 1.5 Factor a perfect square on the left side: (t + -0.75)(t + -0.75) = 1.5 Calculate the square root of the right side: 1.224744871 Break this problem into two subproblems by setting (t + -0.75) equal to 1.224744871 and -1.224744871.Subproblem 1
t + -0.75 = 1.224744871 Simplifying t + -0.75 = 1.224744871 Reorder the terms: -0.75 + t = 1.224744871 Solving -0.75 + t = 1.224744871 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + t = 1.224744871 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + t = 1.224744871 + 0.75 t = 1.224744871 + 0.75 Combine like terms: 1.224744871 + 0.75 = 1.974744871 t = 1.974744871 Simplifying t = 1.974744871Subproblem 2
t + -0.75 = -1.224744871 Simplifying t + -0.75 = -1.224744871 Reorder the terms: -0.75 + t = -1.224744871 Solving -0.75 + t = -1.224744871 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + t = -1.224744871 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + t = -1.224744871 + 0.75 t = -1.224744871 + 0.75 Combine like terms: -1.224744871 + 0.75 = -0.474744871 t = -0.474744871 Simplifying t = -0.474744871Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.974744871, -0.474744871}
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