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Simplifying 0 = -16t2 + 1t + 10 Reorder the terms: 0 = 10 + 1t + -16t2 Solving 0 = 10 + 1t + -16t2 Solving for variable 't'. Combine like terms: 0 + -10 = -10 -10 + -1t + 16t2 = 10 + 1t + -16t2 + -10 + -1t + 16t2 Reorder the terms: -10 + -1t + 16t2 = 10 + -10 + 1t + -1t + -16t2 + 16t2 Combine like terms: 10 + -10 = 0 -10 + -1t + 16t2 = 0 + 1t + -1t + -16t2 + 16t2 -10 + -1t + 16t2 = 1t + -1t + -16t2 + 16t2 Combine like terms: 1t + -1t = 0 -10 + -1t + 16t2 = 0 + -16t2 + 16t2 -10 + -1t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -10 + -1t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.625 + -0.0625t + t2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + -0.0625t + 0.625 + t2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + -0.0625t + t2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + -0.0625t + t2 = 0 + 0.625 -0.0625t + t2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 -0.0625t + t2 = 0.625 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 = 0.625 + 0.0009765625 Reorder the terms: 0.0009765625 + -0.0625t + t2 = 0.625 + 0.0009765625 Combine like terms: 0.625 + 0.0009765625 = 0.6259765625 0.0009765625 + -0.0625t + t2 = 0.6259765625 Factor a perfect square on the left side: (t + -0.03125)(t + -0.03125) = 0.6259765625 Calculate the square root of the right side: 0.791186806 Break this problem into two subproblems by setting (t + -0.03125) equal to 0.791186806 and -0.791186806.Subproblem 1
t + -0.03125 = 0.791186806 Simplifying t + -0.03125 = 0.791186806 Reorder the terms: -0.03125 + t = 0.791186806 Solving -0.03125 + t = 0.791186806 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 = 0.791186806 + 0.03125 Combine like terms: -0.03125 + 0.03125 = 0.00000 0.00000 + t = 0.791186806 + 0.03125 t = 0.791186806 + 0.03125 Combine like terms: 0.791186806 + 0.03125 = 0.822436806 t = 0.822436806 Simplifying t = 0.822436806Subproblem 2
t + -0.03125 = -0.791186806 Simplifying t + -0.03125 = -0.791186806 Reorder the terms: -0.03125 + t = -0.791186806 Solving -0.03125 + t = -0.791186806 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 = -0.791186806 + 0.03125 Combine like terms: -0.03125 + 0.03125 = 0.00000 0.00000 + t = -0.791186806 + 0.03125 t = -0.791186806 + 0.03125 Combine like terms: -0.791186806 + 0.03125 = -0.759936806 t = -0.759936806 Simplifying t = -0.759936806Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.822436806, -0.759936806}
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