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Simplifying 45 + 15t = 1.5t2 Solving 45 + 15t = 1.5t2 Solving for variable 't'. Combine like terms: 1.5t2 + -1.5t2 = 0.0 45 + 15t + -1.5t2 = 0.0 Begin completing the square. Divide all terms by -1.5 the coefficient of the squared term: Divide each side by '-1.5'. -30 + -10t + t2 = 0 Move the constant term to the right: Add '30' to each side of the equation. -30 + -10t + 30 + t2 = 0 + 30 Reorder the terms: -30 + 30 + -10t + t2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + -10t + t2 = 0 + 30 -10t + t2 = 0 + 30 Combine like terms: 0 + 30 = 30 -10t + t2 = 30 The t term is -10t. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10t + 25 + t2 = 30 + 25 Reorder the terms: 25 + -10t + t2 = 30 + 25 Combine like terms: 30 + 25 = 55 25 + -10t + t2 = 55 Factor a perfect square on the left side: (t + -5)(t + -5) = 55 Calculate the square root of the right side: 7.416198487 Break this problem into two subproblems by setting (t + -5) equal to 7.416198487 and -7.416198487.Subproblem 1
t + -5 = 7.416198487 Simplifying t + -5 = 7.416198487 Reorder the terms: -5 + t = 7.416198487 Solving -5 + t = 7.416198487 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + t = 7.416198487 + 5 Combine like terms: -5 + 5 = 0 0 + t = 7.416198487 + 5 t = 7.416198487 + 5 Combine like terms: 7.416198487 + 5 = 12.416198487 t = 12.416198487 Simplifying t = 12.416198487Subproblem 2
t + -5 = -7.416198487 Simplifying t + -5 = -7.416198487 Reorder the terms: -5 + t = -7.416198487 Solving -5 + t = -7.416198487 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + t = -7.416198487 + 5 Combine like terms: -5 + 5 = 0 0 + t = -7.416198487 + 5 t = -7.416198487 + 5 Combine like terms: -7.416198487 + 5 = -2.416198487 t = -2.416198487 Simplifying t = -2.416198487Solution
The solution to the problem is based on the solutions from the subproblems. t = {12.416198487, -2.416198487}
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