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Simplifying 1600 = 3t2 + 60t Reorder the terms: 1600 = 60t + 3t2 Solving 1600 = 60t + 3t2 Solving for variable 't'. Reorder the terms: 1600 + -60t + -3t2 = 60t + -60t + 3t2 + -3t2 Combine like terms: 60t + -60t = 0 1600 + -60t + -3t2 = 0 + 3t2 + -3t2 1600 + -60t + -3t2 = 3t2 + -3t2 Combine like terms: 3t2 + -3t2 = 0 1600 + -60t + -3t2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -533.3333333 + 20t + t2 = 0 Move the constant term to the right: Add '533.3333333' to each side of the equation. -533.3333333 + 20t + 533.3333333 + t2 = 0 + 533.3333333 Reorder the terms: -533.3333333 + 533.3333333 + 20t + t2 = 0 + 533.3333333 Combine like terms: -533.3333333 + 533.3333333 = 0.0000000 0.0000000 + 20t + t2 = 0 + 533.3333333 20t + t2 = 0 + 533.3333333 Combine like terms: 0 + 533.3333333 = 533.3333333 20t + t2 = 533.3333333 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 = 533.3333333 + 100 Reorder the terms: 100 + 20t + t2 = 533.3333333 + 100 Combine like terms: 533.3333333 + 100 = 633.3333333 100 + 20t + t2 = 633.3333333 Factor a perfect square on the left side: (t + 10)(t + 10) = 633.3333333 Calculate the square root of the right side: 25.166114784 Break this problem into two subproblems by setting (t + 10) equal to 25.166114784 and -25.166114784.Subproblem 1
t + 10 = 25.166114784 Simplifying t + 10 = 25.166114784 Reorder the terms: 10 + t = 25.166114784 Solving 10 + t = 25.166114784 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 = 25.166114784 + -10 Combine like terms: 10 + -10 = 0 0 + t = 25.166114784 + -10 t = 25.166114784 + -10 Combine like terms: 25.166114784 + -10 = 15.166114784 t = 15.166114784 Simplifying t = 15.166114784Subproblem 2
t + 10 = -25.166114784 Simplifying t + 10 = -25.166114784 Reorder the terms: 10 + t = -25.166114784 Solving 10 + t = -25.166114784 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 = -25.166114784 + -10 Combine like terms: 10 + -10 = 0 0 + t = -25.166114784 + -10 t = -25.166114784 + -10 Combine like terms: -25.166114784 + -10 = -35.166114784 t = -35.166114784 Simplifying t = -35.166114784Solution
The solution to the problem is based on the solutions from the subproblems. t = {15.166114784, -35.166114784}
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