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Simplifying 0 = -5t2 + 90t + 1 Reorder the terms: 0 = 1 + 90t + -5t2 Solving 0 = 1 + 90t + -5t2 Solving for variable 't'. Combine like terms: 0 + -1 = -1 -1 + -90t + 5t2 = 1 + 90t + -5t2 + -1 + -90t + 5t2 Reorder the terms: -1 + -90t + 5t2 = 1 + -1 + 90t + -90t + -5t2 + 5t2 Combine like terms: 1 + -1 = 0 -1 + -90t + 5t2 = 0 + 90t + -90t + -5t2 + 5t2 -1 + -90t + 5t2 = 90t + -90t + -5t2 + 5t2 Combine like terms: 90t + -90t = 0 -1 + -90t + 5t2 = 0 + -5t2 + 5t2 -1 + -90t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 -1 + -90t + 5t2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.2 + -18t + t2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + -18t + 0.2 + t2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + -18t + t2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + -18t + t2 = 0 + 0.2 -18t + t2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 -18t + t2 = 0.2 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 = 0.2 + 81 Reorder the terms: 81 + -18t + t2 = 0.2 + 81 Combine like terms: 0.2 + 81 = 81.2 81 + -18t + t2 = 81.2 Factor a perfect square on the left side: (t + -9)(t + -9) = 81.2 Calculate the square root of the right side: 9.011104261 Break this problem into two subproblems by setting (t + -9) equal to 9.011104261 and -9.011104261.Subproblem 1
t + -9 = 9.011104261 Simplifying t + -9 = 9.011104261 Reorder the terms: -9 + t = 9.011104261 Solving -9 + t = 9.011104261 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 = 9.011104261 + 9 Combine like terms: -9 + 9 = 0 0 + t = 9.011104261 + 9 t = 9.011104261 + 9 Combine like terms: 9.011104261 + 9 = 18.011104261 t = 18.011104261 Simplifying t = 18.011104261Subproblem 2
t + -9 = -9.011104261 Simplifying t + -9 = -9.011104261 Reorder the terms: -9 + t = -9.011104261 Solving -9 + t = -9.011104261 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 = -9.011104261 + 9 Combine like terms: -9 + 9 = 0 0 + t = -9.011104261 + 9 t = -9.011104261 + 9 Combine like terms: -9.011104261 + 9 = -0.011104261 t = -0.011104261 Simplifying t = -0.011104261Solution
The solution to the problem is based on the solutions from the subproblems. t = {18.011104261, -0.011104261}
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