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Simplifying 0 = (0.3t2) + -6t + 30 Reorder the terms: 0 = 30 + -6t + (0.3t2) Solving 0 = 30 + -6t + (0.3t2) Solving for variable 't'. Combine like terms: 0 + -30 = -30 -30 + 6t + (-0.3t2) = 30 + -6t + (0.3t2) + -30 + 6t + (-0.3t2) Reorder the terms: -30 + 6t + (-0.3t2) = 30 + -30 + -6t + 6t + (0.3t2) + (-0.3t2) Combine like terms: 30 + -30 = 0 -30 + 6t + (-0.3t2) = 0 + -6t + 6t + (0.3t2) + (-0.3t2) -30 + 6t + (-0.3t2) = -6t + 6t + (0.3t2) + (-0.3t2) Combine like terms: -6t + 6t = 0 -30 + 6t + (-0.3t2) = 0 + (0.3t2) + (-0.3t2) -30 + 6t + (-0.3t2) = (0.3t2) + (-0.3t2) Combine like terms: (0.3t2) + (-0.3t2) = 0.0 -30 + 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'. 100 + -20t + t2 = 0 Move the constant term to the right: Add '-100' to each side of the equation. 100 + -20t + -100 + t2 = 0 + -100 Reorder the terms: 100 + -100 + -20t + t2 = 0 + -100 Combine like terms: 100 + -100 = 0 0 + -20t + t2 = 0 + -100 -20t + t2 = 0 + -100 Combine like terms: 0 + -100 = -100 -20t + t2 = -100 The t term is -20t. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20t + 100 + t2 = -100 + 100 Reorder the terms: 100 + -20t + t2 = -100 + 100 Combine like terms: -100 + 100 = 0 100 + -20t + t2 = 0 Factor a perfect square on the left side: ((t) + -10)((t) + -10) = 0 Calculate the square root of the right side: 0 Break this problem into two subproblems by setting ((t) + -10) equal to 0 and 0.Subproblem 1
(t) + -10 = 0 Simplifying (t) + -10 = 0 t + -10 = 0 Reorder the terms: -10 + t = 0 Solving -10 + t = 0 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + t = 0 + 10 Combine like terms: -10 + 10 = 0 0 + t = 0 + 10 t = 0 + 10 Combine like terms: 0 + 10 = 10 t = 10 Simplifying t = 10Subproblem 2
(t) + -10 = 0 Simplifying (t) + -10 = 0 t + -10 = 0 Reorder the terms: -10 + t = 0 Solving -10 + t = 0 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + t = 0 + 10 Combine like terms: -10 + 10 = 0 0 + t = 0 + 10 t = 0 + 10 Combine like terms: 0 + 10 = 10 t = 10 Simplifying t = 10Solution
The solution to the problem is based on the solutions from the subproblems. t = {10, 10}
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