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Simplifying 8 = 0.3t2 + 0.6t + 0.5 Reorder the terms: 8 = 0.5 + 0.6t + 0.3t2 Solving 8 = 0.5 + 0.6t + 0.3t2 Solving for variable 't'. Combine like terms: 8 + -0.5 = 7.5 7.5 + -0.6t + -0.3t2 = 0.5 + 0.6t + 0.3t2 + -0.5 + -0.6t + -0.3t2 Reorder the terms: 7.5 + -0.6t + -0.3t2 = 0.5 + -0.5 + 0.6t + -0.6t + 0.3t2 + -0.3t2 Combine like terms: 0.5 + -0.5 = 0.0 7.5 + -0.6t + -0.3t2 = 0.0 + 0.6t + -0.6t + 0.3t2 + -0.3t2 7.5 + -0.6t + -0.3t2 = 0.6t + -0.6t + 0.3t2 + -0.3t2 Combine like terms: 0.6t + -0.6t = 0.0 7.5 + -0.6t + -0.3t2 = 0.0 + 0.3t2 + -0.3t2 7.5 + -0.6t + -0.3t2 = 0.3t2 + -0.3t2 Combine like terms: 0.3t2 + -0.3t2 = 0.0 7.5 + -0.6t + -0.3t2 = 0.0 Begin completing the square. Divide all terms by -0.3 the coefficient of the squared term: Divide each side by '-0.3'. -25 + 2t + t2 = 0 Move the constant term to the right: Add '25' to each side of the equation. -25 + 2t + 25 + t2 = 0 + 25 Reorder the terms: -25 + 25 + 2t + t2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 2t + t2 = 0 + 25 2t + t2 = 0 + 25 Combine like terms: 0 + 25 = 25 2t + t2 = 25 The t term is 2t. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2t + 1 + t2 = 25 + 1 Reorder the terms: 1 + 2t + t2 = 25 + 1 Combine like terms: 25 + 1 = 26 1 + 2t + t2 = 26 Factor a perfect square on the left side: (t + 1)(t + 1) = 26 Calculate the square root of the right side: 5.099019514 Break this problem into two subproblems by setting (t + 1) equal to 5.099019514 and -5.099019514.Subproblem 1
t + 1 = 5.099019514 Simplifying t + 1 = 5.099019514 Reorder the terms: 1 + t = 5.099019514 Solving 1 + t = 5.099019514 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + t = 5.099019514 + -1 Combine like terms: 1 + -1 = 0 0 + t = 5.099019514 + -1 t = 5.099019514 + -1 Combine like terms: 5.099019514 + -1 = 4.099019514 t = 4.099019514 Simplifying t = 4.099019514Subproblem 2
t + 1 = -5.099019514 Simplifying t + 1 = -5.099019514 Reorder the terms: 1 + t = -5.099019514 Solving 1 + t = -5.099019514 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + t = -5.099019514 + -1 Combine like terms: 1 + -1 = 0 0 + t = -5.099019514 + -1 t = -5.099019514 + -1 Combine like terms: -5.099019514 + -1 = -6.099019514 t = -6.099019514 Simplifying t = -6.099019514Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.099019514, -6.099019514}
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