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Simplifying -16t2 + 105t + 200 = 0 Reorder the terms: 200 + 105t + -16t2 = 0 Solving 200 + 105t + -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 + -6.5625t + t2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + -6.5625t + 12.5 + t2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + -6.5625t + t2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + -6.5625t + t2 = 0 + 12.5 -6.5625t + t2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 -6.5625t + t2 = 12.5 The t term is -6.5625t. Take half its coefficient (-3.28125). Square it (10.76660156) and add it to both sides. Add '10.76660156' to each side of the equation. -6.5625t + 10.76660156 + t2 = 12.5 + 10.76660156 Reorder the terms: 10.76660156 + -6.5625t + t2 = 12.5 + 10.76660156 Combine like terms: 12.5 + 10.76660156 = 23.26660156 10.76660156 + -6.5625t + t2 = 23.26660156 Factor a perfect square on the left side: (t + -3.28125)(t + -3.28125) = 23.26660156 Calculate the square root of the right side: 4.823546575 Break this problem into two subproblems by setting (t + -3.28125) equal to 4.823546575 and -4.823546575.Subproblem 1
t + -3.28125 = 4.823546575 Simplifying t + -3.28125 = 4.823546575 Reorder the terms: -3.28125 + t = 4.823546575 Solving -3.28125 + t = 4.823546575 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.28125' to each side of the equation. -3.28125 + 3.28125 + t = 4.823546575 + 3.28125 Combine like terms: -3.28125 + 3.28125 = 0.00000 0.00000 + t = 4.823546575 + 3.28125 t = 4.823546575 + 3.28125 Combine like terms: 4.823546575 + 3.28125 = 8.104796575 t = 8.104796575 Simplifying t = 8.104796575Subproblem 2
t + -3.28125 = -4.823546575 Simplifying t + -3.28125 = -4.823546575 Reorder the terms: -3.28125 + t = -4.823546575 Solving -3.28125 + t = -4.823546575 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.28125' to each side of the equation. -3.28125 + 3.28125 + t = -4.823546575 + 3.28125 Combine like terms: -3.28125 + 3.28125 = 0.00000 0.00000 + t = -4.823546575 + 3.28125 t = -4.823546575 + 3.28125 Combine like terms: -4.823546575 + 3.28125 = -1.542296575 t = -1.542296575 Simplifying t = -1.542296575Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.104796575, -1.542296575}
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