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Simplifying -16t2 + 45t + 200 = 0 Reorder the terms: 200 + 45t + -16t2 = 0 Solving 200 + 45t + -16t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -12.5 + -2.8125t + t2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + -2.8125t + 12.5 + t2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + -2.8125t + t2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + -2.8125t + t2 = 0 + 12.5 -2.8125t + t2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 -2.8125t + t2 = 12.5 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 = 12.5 + 1.977539063 Reorder the terms: 1.977539063 + -2.8125t + t2 = 12.5 + 1.977539063 Combine like terms: 12.5 + 1.977539063 = 14.477539063 1.977539063 + -2.8125t + t2 = 14.477539063 Factor a perfect square on the left side: (t + -1.40625)(t + -1.40625) = 14.477539063 Calculate the square root of the right side: 3.804936144 Break this problem into two subproblems by setting (t + -1.40625) equal to 3.804936144 and -3.804936144.Subproblem 1
t + -1.40625 = 3.804936144 Simplifying t + -1.40625 = 3.804936144 Reorder the terms: -1.40625 + t = 3.804936144 Solving -1.40625 + t = 3.804936144 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 = 3.804936144 + 1.40625 Combine like terms: -1.40625 + 1.40625 = 0.00000 0.00000 + t = 3.804936144 + 1.40625 t = 3.804936144 + 1.40625 Combine like terms: 3.804936144 + 1.40625 = 5.211186144 t = 5.211186144 Simplifying t = 5.211186144Subproblem 2
t + -1.40625 = -3.804936144 Simplifying t + -1.40625 = -3.804936144 Reorder the terms: -1.40625 + t = -3.804936144 Solving -1.40625 + t = -3.804936144 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 = -3.804936144 + 1.40625 Combine like terms: -1.40625 + 1.40625 = 0.00000 0.00000 + t = -3.804936144 + 1.40625 t = -3.804936144 + 1.40625 Combine like terms: -3.804936144 + 1.40625 = -2.398686144 t = -2.398686144 Simplifying t = -2.398686144Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.211186144, -2.398686144}
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