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Simplifying 0 = 141 + -21t + -16t2 Solving 0 = 141 + -21t + -16t2 Solving for variable 't'. Combine like terms: 0 + -141 = -141 -141 + 21t + 16t2 = 141 + -21t + -16t2 + -141 + 21t + 16t2 Reorder the terms: -141 + 21t + 16t2 = 141 + -141 + -21t + 21t + -16t2 + 16t2 Combine like terms: 141 + -141 = 0 -141 + 21t + 16t2 = 0 + -21t + 21t + -16t2 + 16t2 -141 + 21t + 16t2 = -21t + 21t + -16t2 + 16t2 Combine like terms: -21t + 21t = 0 -141 + 21t + 16t2 = 0 + -16t2 + 16t2 -141 + 21t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -141 + 21t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -8.8125 + 1.3125t + t2 = 0 Move the constant term to the right: Add '8.8125' to each side of the equation. -8.8125 + 1.3125t + 8.8125 + t2 = 0 + 8.8125 Reorder the terms: -8.8125 + 8.8125 + 1.3125t + t2 = 0 + 8.8125 Combine like terms: -8.8125 + 8.8125 = 0.0000 0.0000 + 1.3125t + t2 = 0 + 8.8125 1.3125t + t2 = 0 + 8.8125 Combine like terms: 0 + 8.8125 = 8.8125 1.3125t + t2 = 8.8125 The t term is 1.3125t. Take half its coefficient (0.65625). Square it (0.4306640625) and add it to both sides. Add '0.4306640625' to each side of the equation. 1.3125t + 0.4306640625 + t2 = 8.8125 + 0.4306640625 Reorder the terms: 0.4306640625 + 1.3125t + t2 = 8.8125 + 0.4306640625 Combine like terms: 8.8125 + 0.4306640625 = 9.2431640625 0.4306640625 + 1.3125t + t2 = 9.2431640625 Factor a perfect square on the left side: (t + 0.65625)(t + 0.65625) = 9.2431640625 Calculate the square root of the right side: 3.040257236 Break this problem into two subproblems by setting (t + 0.65625) equal to 3.040257236 and -3.040257236.Subproblem 1
t + 0.65625 = 3.040257236 Simplifying t + 0.65625 = 3.040257236 Reorder the terms: 0.65625 + t = 3.040257236 Solving 0.65625 + t = 3.040257236 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.65625' to each side of the equation. 0.65625 + -0.65625 + t = 3.040257236 + -0.65625 Combine like terms: 0.65625 + -0.65625 = 0.00000 0.00000 + t = 3.040257236 + -0.65625 t = 3.040257236 + -0.65625 Combine like terms: 3.040257236 + -0.65625 = 2.384007236 t = 2.384007236 Simplifying t = 2.384007236Subproblem 2
t + 0.65625 = -3.040257236 Simplifying t + 0.65625 = -3.040257236 Reorder the terms: 0.65625 + t = -3.040257236 Solving 0.65625 + t = -3.040257236 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.65625' to each side of the equation. 0.65625 + -0.65625 + t = -3.040257236 + -0.65625 Combine like terms: 0.65625 + -0.65625 = 0.00000 0.00000 + t = -3.040257236 + -0.65625 t = -3.040257236 + -0.65625 Combine like terms: -3.040257236 + -0.65625 = -3.696507236 t = -3.696507236 Simplifying t = -3.696507236Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.384007236, -3.696507236}
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