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Simplifying 263t + -16t2 = 8 Solving 263t + -16t2 = 8 Solving for variable 't'. Reorder the terms: -8 + 263t + -16t2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + 263t + -16t2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. 0.5 + -16.4375t + t2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -16.4375t + -0.5 + t2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -16.4375t + t2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -16.4375t + t2 = 0 + -0.5 -16.4375t + t2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -16.4375t + t2 = -0.5 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 = -0.5 + 67.54785156 Reorder the terms: 67.54785156 + -16.4375t + t2 = -0.5 + 67.54785156 Combine like terms: -0.5 + 67.54785156 = 67.04785156 67.54785156 + -16.4375t + t2 = 67.04785156 Factor a perfect square on the left side: (t + -8.21875)(t + -8.21875) = 67.04785156 Calculate the square root of the right side: 8.188275249 Break this problem into two subproblems by setting (t + -8.21875) equal to 8.188275249 and -8.188275249.Subproblem 1
t + -8.21875 = 8.188275249 Simplifying t + -8.21875 = 8.188275249 Reorder the terms: -8.21875 + t = 8.188275249 Solving -8.21875 + t = 8.188275249 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 = 8.188275249 + 8.21875 Combine like terms: -8.21875 + 8.21875 = 0.00000 0.00000 + t = 8.188275249 + 8.21875 t = 8.188275249 + 8.21875 Combine like terms: 8.188275249 + 8.21875 = 16.407025249 t = 16.407025249 Simplifying t = 16.407025249Subproblem 2
t + -8.21875 = -8.188275249 Simplifying t + -8.21875 = -8.188275249 Reorder the terms: -8.21875 + t = -8.188275249 Solving -8.21875 + t = -8.188275249 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 = -8.188275249 + 8.21875 Combine like terms: -8.21875 + 8.21875 = 0.00000 0.00000 + t = -8.188275249 + 8.21875 t = -8.188275249 + 8.21875 Combine like terms: -8.188275249 + 8.21875 = 0.030474751 t = 0.030474751 Simplifying t = 0.030474751Solution
The solution to the problem is based on the solutions from the subproblems. t = {16.407025249, 0.030474751}
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