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Simplifying 16t2 + -1t + -1250 = 0 Reorder the terms: -1250 + -1t + 16t2 = 0 Solving -1250 + -1t + 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'. -78.125 + -0.0625t + t2 = 0 Move the constant term to the right: Add '78.125' to each side of the equation. -78.125 + -0.0625t + 78.125 + t2 = 0 + 78.125 Reorder the terms: -78.125 + 78.125 + -0.0625t + t2 = 0 + 78.125 Combine like terms: -78.125 + 78.125 = 0.000 0.000 + -0.0625t + t2 = 0 + 78.125 -0.0625t + t2 = 0 + 78.125 Combine like terms: 0 + 78.125 = 78.125 -0.0625t + t2 = 78.125 The t term is -0.0625t. Take half its coefficient (-0.03125). Square it (0.0009765625) and add it to both sides. Add '0.0009765625' to each side of the equation. -0.0625t + 0.0009765625 + t2 = 78.125 + 0.0009765625 Reorder the terms: 0.0009765625 + -0.0625t + t2 = 78.125 + 0.0009765625 Combine like terms: 78.125 + 0.0009765625 = 78.1259765625 0.0009765625 + -0.0625t + t2 = 78.1259765625 Factor a perfect square on the left side: (t + -0.03125)(t + -0.03125) = 78.1259765625 Calculate the square root of the right side: 8.838890007 Break this problem into two subproblems by setting (t + -0.03125) equal to 8.838890007 and -8.838890007.Subproblem 1
t + -0.03125 = 8.838890007 Simplifying t + -0.03125 = 8.838890007 Reorder the terms: -0.03125 + t = 8.838890007 Solving -0.03125 + t = 8.838890007 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.03125' to each side of the equation. -0.03125 + 0.03125 + t = 8.838890007 + 0.03125 Combine like terms: -0.03125 + 0.03125 = 0.00000 0.00000 + t = 8.838890007 + 0.03125 t = 8.838890007 + 0.03125 Combine like terms: 8.838890007 + 0.03125 = 8.870140007 t = 8.870140007 Simplifying t = 8.870140007Subproblem 2
t + -0.03125 = -8.838890007 Simplifying t + -0.03125 = -8.838890007 Reorder the terms: -0.03125 + t = -8.838890007 Solving -0.03125 + t = -8.838890007 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.03125' to each side of the equation. -0.03125 + 0.03125 + t = -8.838890007 + 0.03125 Combine like terms: -0.03125 + 0.03125 = 0.00000 0.00000 + t = -8.838890007 + 0.03125 t = -8.838890007 + 0.03125 Combine like terms: -8.838890007 + 0.03125 = -8.807640007 t = -8.807640007 Simplifying t = -8.807640007Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.870140007, -8.807640007}
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