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Simplifying 16t2 + -3t + -10 = 0 Reorder the terms: -10 + -3t + 16t2 = 0 Solving -10 + -3t + 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'. -0.625 + -0.1875t + t2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + -0.1875t + 0.625 + t2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + -0.1875t + t2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + -0.1875t + t2 = 0 + 0.625 -0.1875t + t2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 -0.1875t + t2 = 0.625 The t term is -0.1875t. Take half its coefficient (-0.09375). Square it (0.0087890625) and add it to both sides. Add '0.0087890625' to each side of the equation. -0.1875t + 0.0087890625 + t2 = 0.625 + 0.0087890625 Reorder the terms: 0.0087890625 + -0.1875t + t2 = 0.625 + 0.0087890625 Combine like terms: 0.625 + 0.0087890625 = 0.6337890625 0.0087890625 + -0.1875t + t2 = 0.6337890625 Factor a perfect square on the left side: (t + -0.09375)(t + -0.09375) = 0.6337890625 Calculate the square root of the right side: 0.7961087 Break this problem into two subproblems by setting (t + -0.09375) equal to 0.7961087 and -0.7961087.Subproblem 1
t + -0.09375 = 0.7961087 Simplifying t + -0.09375 = 0.7961087 Reorder the terms: -0.09375 + t = 0.7961087 Solving -0.09375 + t = 0.7961087 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.09375' to each side of the equation. -0.09375 + 0.09375 + t = 0.7961087 + 0.09375 Combine like terms: -0.09375 + 0.09375 = 0.00000 0.00000 + t = 0.7961087 + 0.09375 t = 0.7961087 + 0.09375 Combine like terms: 0.7961087 + 0.09375 = 0.8898587 t = 0.8898587 Simplifying t = 0.8898587Subproblem 2
t + -0.09375 = -0.7961087 Simplifying t + -0.09375 = -0.7961087 Reorder the terms: -0.09375 + t = -0.7961087 Solving -0.09375 + t = -0.7961087 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.09375' to each side of the equation. -0.09375 + 0.09375 + t = -0.7961087 + 0.09375 Combine like terms: -0.09375 + 0.09375 = 0.00000 0.00000 + t = -0.7961087 + 0.09375 t = -0.7961087 + 0.09375 Combine like terms: -0.7961087 + 0.09375 = -0.7023587 t = -0.7023587 Simplifying t = -0.7023587Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.8898587, -0.7023587}
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