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Simplifying 30t + -0.3t2 = 5 Solving 30t + -0.3t2 = 5 Solving for variable 't'. Reorder the terms: -5 + 30t + -0.3t2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + 30t + -0.3t2 = 0 Begin completing the square. Divide all terms by -0.3 the coefficient of the squared term: Divide each side by '-0.3'. 16.66666667 + -100t + t2 = 0 Move the constant term to the right: Add '-16.66666667' to each side of the equation. 16.66666667 + -100t + -16.66666667 + t2 = 0 + -16.66666667 Reorder the terms: 16.66666667 + -16.66666667 + -100t + t2 = 0 + -16.66666667 Combine like terms: 16.66666667 + -16.66666667 = 0.00000000 0.00000000 + -100t + t2 = 0 + -16.66666667 -100t + t2 = 0 + -16.66666667 Combine like terms: 0 + -16.66666667 = -16.66666667 -100t + t2 = -16.66666667 The t term is -100t. Take half its coefficient (-50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. -100t + 2500 + t2 = -16.66666667 + 2500 Reorder the terms: 2500 + -100t + t2 = -16.66666667 + 2500 Combine like terms: -16.66666667 + 2500 = 2483.33333333 2500 + -100t + t2 = 2483.33333333 Factor a perfect square on the left side: (t + -50)(t + -50) = 2483.33333333 Calculate the square root of the right side: 49.833054626 Break this problem into two subproblems by setting (t + -50) equal to 49.833054626 and -49.833054626.Subproblem 1
t + -50 = 49.833054626 Simplifying t + -50 = 49.833054626 Reorder the terms: -50 + t = 49.833054626 Solving -50 + t = 49.833054626 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + t = 49.833054626 + 50 Combine like terms: -50 + 50 = 0 0 + t = 49.833054626 + 50 t = 49.833054626 + 50 Combine like terms: 49.833054626 + 50 = 99.833054626 t = 99.833054626 Simplifying t = 99.833054626Subproblem 2
t + -50 = -49.833054626 Simplifying t + -50 = -49.833054626 Reorder the terms: -50 + t = -49.833054626 Solving -50 + t = -49.833054626 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + t = -49.833054626 + 50 Combine like terms: -50 + 50 = 0 0 + t = -49.833054626 + 50 t = -49.833054626 + 50 Combine like terms: -49.833054626 + 50 = 0.166945374 t = 0.166945374 Simplifying t = 0.166945374Solution
The solution to the problem is based on the solutions from the subproblems. t = {99.833054626, 0.166945374}
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