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Simplifying 0 = -16t2 + 45t + 1200 Reorder the terms: 0 = 1200 + 45t + -16t2 Solving 0 = 1200 + 45t + -16t2 Solving for variable 't'. Combine like terms: 0 + -1200 = -1200 -1200 + -45t + 16t2 = 1200 + 45t + -16t2 + -1200 + -45t + 16t2 Reorder the terms: -1200 + -45t + 16t2 = 1200 + -1200 + 45t + -45t + -16t2 + 16t2 Combine like terms: 1200 + -1200 = 0 -1200 + -45t + 16t2 = 0 + 45t + -45t + -16t2 + 16t2 -1200 + -45t + 16t2 = 45t + -45t + -16t2 + 16t2 Combine like terms: 45t + -45t = 0 -1200 + -45t + 16t2 = 0 + -16t2 + 16t2 -1200 + -45t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -1200 + -45t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -75 + -2.8125t + t2 = 0 Move the constant term to the right: Add '75' to each side of the equation. -75 + -2.8125t + 75 + t2 = 0 + 75 Reorder the terms: -75 + 75 + -2.8125t + t2 = 0 + 75 Combine like terms: -75 + 75 = 0 0 + -2.8125t + t2 = 0 + 75 -2.8125t + t2 = 0 + 75 Combine like terms: 0 + 75 = 75 -2.8125t + t2 = 75 The t term is -2.8125t. Take half its coefficient (-1.40625). Square it (1.977539063) and add it to both sides. Add '1.977539063' to each side of the equation. -2.8125t + 1.977539063 + t2 = 75 + 1.977539063 Reorder the terms: 1.977539063 + -2.8125t + t2 = 75 + 1.977539063 Combine like terms: 75 + 1.977539063 = 76.977539063 1.977539063 + -2.8125t + t2 = 76.977539063 Factor a perfect square on the left side: (t + -1.40625)(t + -1.40625) = 76.977539063 Calculate the square root of the right side: 8.773684463 Break this problem into two subproblems by setting (t + -1.40625) equal to 8.773684463 and -8.773684463.Subproblem 1
t + -1.40625 = 8.773684463 Simplifying t + -1.40625 = 8.773684463 Reorder the terms: -1.40625 + t = 8.773684463 Solving -1.40625 + t = 8.773684463 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.40625' to each side of the equation. -1.40625 + 1.40625 + t = 8.773684463 + 1.40625 Combine like terms: -1.40625 + 1.40625 = 0.00000 0.00000 + t = 8.773684463 + 1.40625 t = 8.773684463 + 1.40625 Combine like terms: 8.773684463 + 1.40625 = 10.179934463 t = 10.179934463 Simplifying t = 10.179934463Subproblem 2
t + -1.40625 = -8.773684463 Simplifying t + -1.40625 = -8.773684463 Reorder the terms: -1.40625 + t = -8.773684463 Solving -1.40625 + t = -8.773684463 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.40625' to each side of the equation. -1.40625 + 1.40625 + t = -8.773684463 + 1.40625 Combine like terms: -1.40625 + 1.40625 = 0.00000 0.00000 + t = -8.773684463 + 1.40625 t = -8.773684463 + 1.40625 Combine like terms: -8.773684463 + 1.40625 = -7.367434463 t = -7.367434463 Simplifying t = -7.367434463Solution
The solution to the problem is based on the solutions from the subproblems. t = {10.179934463, -7.367434463}
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