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Simplifying 263t + -16t2 = 10 Solving 263t + -16t2 = 10 Solving for variable 't'. Reorder the terms: -10 + 263t + -16t2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + 263t + -16t2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. 0.625 + -16.4375t + t2 = 0 Move the constant term to the right: Add '-0.625' to each side of the equation. 0.625 + -16.4375t + -0.625 + t2 = 0 + -0.625 Reorder the terms: 0.625 + -0.625 + -16.4375t + t2 = 0 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + -16.4375t + t2 = 0 + -0.625 -16.4375t + t2 = 0 + -0.625 Combine like terms: 0 + -0.625 = -0.625 -16.4375t + t2 = -0.625 The t term is -16.4375t. Take half its coefficient (-8.21875). Square it (67.54785156) and add it to both sides. Add '67.54785156' to each side of the equation. -16.4375t + 67.54785156 + t2 = -0.625 + 67.54785156 Reorder the terms: 67.54785156 + -16.4375t + t2 = -0.625 + 67.54785156 Combine like terms: -0.625 + 67.54785156 = 66.92285156 67.54785156 + -16.4375t + t2 = 66.92285156 Factor a perfect square on the left side: (t + -8.21875)(t + -8.21875) = 66.92285156 Calculate the square root of the right side: 8.180638823 Break this problem into two subproblems by setting (t + -8.21875) equal to 8.180638823 and -8.180638823.Subproblem 1
t + -8.21875 = 8.180638823 Simplifying t + -8.21875 = 8.180638823 Reorder the terms: -8.21875 + t = 8.180638823 Solving -8.21875 + t = 8.180638823 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '8.21875' to each side of the equation. -8.21875 + 8.21875 + t = 8.180638823 + 8.21875 Combine like terms: -8.21875 + 8.21875 = 0.00000 0.00000 + t = 8.180638823 + 8.21875 t = 8.180638823 + 8.21875 Combine like terms: 8.180638823 + 8.21875 = 16.399388823 t = 16.399388823 Simplifying t = 16.399388823Subproblem 2
t + -8.21875 = -8.180638823 Simplifying t + -8.21875 = -8.180638823 Reorder the terms: -8.21875 + t = -8.180638823 Solving -8.21875 + t = -8.180638823 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '8.21875' to each side of the equation. -8.21875 + 8.21875 + t = -8.180638823 + 8.21875 Combine like terms: -8.21875 + 8.21875 = 0.00000 0.00000 + t = -8.180638823 + 8.21875 t = -8.180638823 + 8.21875 Combine like terms: -8.180638823 + 8.21875 = 0.038111177 t = 0.038111177 Simplifying t = 0.038111177Solution
The solution to the problem is based on the solutions from the subproblems. t = {16.399388823, 0.038111177}
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