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Simplifying 0 = -5t2 + 8t + -1 Reorder the terms: 0 = -1 + 8t + -5t2 Solving 0 = -1 + 8t + -5t2 Solving for variable 't'. Combine like terms: 0 + 1 = 1 1 + -8t + 5t2 = -1 + 8t + -5t2 + 1 + -8t + 5t2 Reorder the terms: 1 + -8t + 5t2 = -1 + 1 + 8t + -8t + -5t2 + 5t2 Combine like terms: -1 + 1 = 0 1 + -8t + 5t2 = 0 + 8t + -8t + -5t2 + 5t2 1 + -8t + 5t2 = 8t + -8t + -5t2 + 5t2 Combine like terms: 8t + -8t = 0 1 + -8t + 5t2 = 0 + -5t2 + 5t2 1 + -8t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 1 + -8t + 5t2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.2 + -1.6t + t2 = 0 Move the constant term to the right: Add '-0.2' to each side of the equation. 0.2 + -1.6t + -0.2 + t2 = 0 + -0.2 Reorder the terms: 0.2 + -0.2 + -1.6t + t2 = 0 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + -1.6t + t2 = 0 + -0.2 -1.6t + t2 = 0 + -0.2 Combine like terms: 0 + -0.2 = -0.2 -1.6t + t2 = -0.2 The t term is -1.6t. Take half its coefficient (-0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. -1.6t + 0.64 + t2 = -0.2 + 0.64 Reorder the terms: 0.64 + -1.6t + t2 = -0.2 + 0.64 Combine like terms: -0.2 + 0.64 = 0.44 0.64 + -1.6t + t2 = 0.44 Factor a perfect square on the left side: (t + -0.8)(t + -0.8) = 0.44 Calculate the square root of the right side: 0.663324958 Break this problem into two subproblems by setting (t + -0.8) equal to 0.663324958 and -0.663324958.Subproblem 1
t + -0.8 = 0.663324958 Simplifying t + -0.8 = 0.663324958 Reorder the terms: -0.8 + t = 0.663324958 Solving -0.8 + t = 0.663324958 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + t = 0.663324958 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + t = 0.663324958 + 0.8 t = 0.663324958 + 0.8 Combine like terms: 0.663324958 + 0.8 = 1.463324958 t = 1.463324958 Simplifying t = 1.463324958Subproblem 2
t + -0.8 = -0.663324958 Simplifying t + -0.8 = -0.663324958 Reorder the terms: -0.8 + t = -0.663324958 Solving -0.8 + t = -0.663324958 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + t = -0.663324958 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + t = -0.663324958 + 0.8 t = -0.663324958 + 0.8 Combine like terms: -0.663324958 + 0.8 = 0.136675042 t = 0.136675042 Simplifying t = 0.136675042Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.463324958, 0.136675042}
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