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Simplifying 12t + -0.6t2 + -30 = 0 Reorder the terms: -30 + 12t + -0.6t2 = 0 Solving -30 + 12t + -0.6t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -0.6 the coefficient of the squared term: Divide each side by '-0.6'. 50 + -20t + t2 = 0 Move the constant term to the right: Add '-50' to each side of the equation. 50 + -20t + -50 + t2 = 0 + -50 Reorder the terms: 50 + -50 + -20t + t2 = 0 + -50 Combine like terms: 50 + -50 = 0 0 + -20t + t2 = 0 + -50 -20t + t2 = 0 + -50 Combine like terms: 0 + -50 = -50 -20t + t2 = -50 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 = -50 + 100 Reorder the terms: 100 + -20t + t2 = -50 + 100 Combine like terms: -50 + 100 = 50 100 + -20t + t2 = 50 Factor a perfect square on the left side: (t + -10)(t + -10) = 50 Calculate the square root of the right side: 7.071067812 Break this problem into two subproblems by setting (t + -10) equal to 7.071067812 and -7.071067812.Subproblem 1
t + -10 = 7.071067812 Simplifying t + -10 = 7.071067812 Reorder the terms: -10 + t = 7.071067812 Solving -10 + t = 7.071067812 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 = 7.071067812 + 10 Combine like terms: -10 + 10 = 0 0 + t = 7.071067812 + 10 t = 7.071067812 + 10 Combine like terms: 7.071067812 + 10 = 17.071067812 t = 17.071067812 Simplifying t = 17.071067812Subproblem 2
t + -10 = -7.071067812 Simplifying t + -10 = -7.071067812 Reorder the terms: -10 + t = -7.071067812 Solving -10 + t = -7.071067812 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 = -7.071067812 + 10 Combine like terms: -10 + 10 = 0 0 + t = -7.071067812 + 10 t = -7.071067812 + 10 Combine like terms: -7.071067812 + 10 = 2.928932188 t = 2.928932188 Simplifying t = 2.928932188Solution
The solution to the problem is based on the solutions from the subproblems. t = {17.071067812, 2.928932188}
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