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Simplifying 8 = -5t2 + 90t Reorder the terms: 8 = 90t + -5t2 Solving 8 = 90t + -5t2 Solving for variable 't'. Reorder the terms: 8 + -90t + 5t2 = 90t + -90t + -5t2 + 5t2 Combine like terms: 90t + -90t = 0 8 + -90t + 5t2 = 0 + -5t2 + 5t2 8 + -90t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 8 + -90t + 5t2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.6 + -18t + t2 = 0 Move the constant term to the right: Add '-1.6' to each side of the equation. 1.6 + -18t + -1.6 + t2 = 0 + -1.6 Reorder the terms: 1.6 + -1.6 + -18t + t2 = 0 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + -18t + t2 = 0 + -1.6 -18t + t2 = 0 + -1.6 Combine like terms: 0 + -1.6 = -1.6 -18t + t2 = -1.6 The t term is -18t. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18t + 81 + t2 = -1.6 + 81 Reorder the terms: 81 + -18t + t2 = -1.6 + 81 Combine like terms: -1.6 + 81 = 79.4 81 + -18t + t2 = 79.4 Factor a perfect square on the left side: (t + -9)(t + -9) = 79.4 Calculate the square root of the right side: 8.910667764 Break this problem into two subproblems by setting (t + -9) equal to 8.910667764 and -8.910667764.Subproblem 1
t + -9 = 8.910667764 Simplifying t + -9 = 8.910667764 Reorder the terms: -9 + t = 8.910667764 Solving -9 + t = 8.910667764 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + t = 8.910667764 + 9 Combine like terms: -9 + 9 = 0 0 + t = 8.910667764 + 9 t = 8.910667764 + 9 Combine like terms: 8.910667764 + 9 = 17.910667764 t = 17.910667764 Simplifying t = 17.910667764Subproblem 2
t + -9 = -8.910667764 Simplifying t + -9 = -8.910667764 Reorder the terms: -9 + t = -8.910667764 Solving -9 + t = -8.910667764 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + t = -8.910667764 + 9 Combine like terms: -9 + 9 = 0 0 + t = -8.910667764 + 9 t = -8.910667764 + 9 Combine like terms: -8.910667764 + 9 = 0.089332236 t = 0.089332236 Simplifying t = 0.089332236Solution
The solution to the problem is based on the solutions from the subproblems. t = {17.910667764, 0.089332236}
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