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Simplifying t2 + -24t + -49 = 0 Reorder the terms: -49 + -24t + t2 = 0 Solving -49 + -24t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '49' to each side of the equation. -49 + -24t + 49 + t2 = 0 + 49 Reorder the terms: -49 + 49 + -24t + t2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + -24t + t2 = 0 + 49 -24t + t2 = 0 + 49 Combine like terms: 0 + 49 = 49 -24t + t2 = 49 The t term is -24t. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24t + 144 + t2 = 49 + 144 Reorder the terms: 144 + -24t + t2 = 49 + 144 Combine like terms: 49 + 144 = 193 144 + -24t + t2 = 193 Factor a perfect square on the left side: (t + -12)(t + -12) = 193 Calculate the square root of the right side: 13.892443989 Break this problem into two subproblems by setting (t + -12) equal to 13.892443989 and -13.892443989.Subproblem 1
t + -12 = 13.892443989 Simplifying t + -12 = 13.892443989 Reorder the terms: -12 + t = 13.892443989 Solving -12 + t = 13.892443989 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + t = 13.892443989 + 12 Combine like terms: -12 + 12 = 0 0 + t = 13.892443989 + 12 t = 13.892443989 + 12 Combine like terms: 13.892443989 + 12 = 25.892443989 t = 25.892443989 Simplifying t = 25.892443989Subproblem 2
t + -12 = -13.892443989 Simplifying t + -12 = -13.892443989 Reorder the terms: -12 + t = -13.892443989 Solving -12 + t = -13.892443989 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + t = -13.892443989 + 12 Combine like terms: -12 + 12 = 0 0 + t = -13.892443989 + 12 t = -13.892443989 + 12 Combine like terms: -13.892443989 + 12 = -1.892443989 t = -1.892443989 Simplifying t = -1.892443989Solution
The solution to the problem is based on the solutions from the subproblems. t = {25.892443989, -1.892443989}
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