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Simplifying 0 = -16t2 + 10t + 3 Reorder the terms: 0 = 3 + 10t + -16t2 Solving 0 = 3 + 10t + -16t2 Solving for variable 't'. Combine like terms: 0 + -3 = -3 -3 + -10t + 16t2 = 3 + 10t + -16t2 + -3 + -10t + 16t2 Reorder the terms: -3 + -10t + 16t2 = 3 + -3 + 10t + -10t + -16t2 + 16t2 Combine like terms: 3 + -3 = 0 -3 + -10t + 16t2 = 0 + 10t + -10t + -16t2 + 16t2 -3 + -10t + 16t2 = 10t + -10t + -16t2 + 16t2 Combine like terms: 10t + -10t = 0 -3 + -10t + 16t2 = 0 + -16t2 + 16t2 -3 + -10t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -3 + -10t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.1875 + -0.625t + t2 = 0 Move the constant term to the right: Add '0.1875' to each side of the equation. -0.1875 + -0.625t + 0.1875 + t2 = 0 + 0.1875 Reorder the terms: -0.1875 + 0.1875 + -0.625t + t2 = 0 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + -0.625t + t2 = 0 + 0.1875 -0.625t + t2 = 0 + 0.1875 Combine like terms: 0 + 0.1875 = 0.1875 -0.625t + t2 = 0.1875 The t term is -0.625t. Take half its coefficient (-0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. -0.625t + 0.09765625 + t2 = 0.1875 + 0.09765625 Reorder the terms: 0.09765625 + -0.625t + t2 = 0.1875 + 0.09765625 Combine like terms: 0.1875 + 0.09765625 = 0.28515625 0.09765625 + -0.625t + t2 = 0.28515625 Factor a perfect square on the left side: (t + -0.3125)(t + -0.3125) = 0.28515625 Calculate the square root of the right side: 0.534000234 Break this problem into two subproblems by setting (t + -0.3125) equal to 0.534000234 and -0.534000234.Subproblem 1
t + -0.3125 = 0.534000234 Simplifying t + -0.3125 = 0.534000234 Reorder the terms: -0.3125 + t = 0.534000234 Solving -0.3125 + t = 0.534000234 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + t = 0.534000234 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + t = 0.534000234 + 0.3125 t = 0.534000234 + 0.3125 Combine like terms: 0.534000234 + 0.3125 = 0.846500234 t = 0.846500234 Simplifying t = 0.846500234Subproblem 2
t + -0.3125 = -0.534000234 Simplifying t + -0.3125 = -0.534000234 Reorder the terms: -0.3125 + t = -0.534000234 Solving -0.3125 + t = -0.534000234 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + t = -0.534000234 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + t = -0.534000234 + 0.3125 t = -0.534000234 + 0.3125 Combine like terms: -0.534000234 + 0.3125 = -0.221500234 t = -0.221500234 Simplifying t = -0.221500234Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.846500234, -0.221500234}
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