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Simplifying t2 + -28t + -27 = 0 Reorder the terms: -27 + -28t + t2 = 0 Solving -27 + -28t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '27' to each side of the equation. -27 + -28t + 27 + t2 = 0 + 27 Reorder the terms: -27 + 27 + -28t + t2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + -28t + t2 = 0 + 27 -28t + t2 = 0 + 27 Combine like terms: 0 + 27 = 27 -28t + t2 = 27 The t term is -28t. Take half its coefficient (-14). Square it (196) and add it to both sides. Add '196' to each side of the equation. -28t + 196 + t2 = 27 + 196 Reorder the terms: 196 + -28t + t2 = 27 + 196 Combine like terms: 27 + 196 = 223 196 + -28t + t2 = 223 Factor a perfect square on the left side: (t + -14)(t + -14) = 223 Calculate the square root of the right side: 14.933184523 Break this problem into two subproblems by setting (t + -14) equal to 14.933184523 and -14.933184523.Subproblem 1
t + -14 = 14.933184523 Simplifying t + -14 = 14.933184523 Reorder the terms: -14 + t = 14.933184523 Solving -14 + t = 14.933184523 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + t = 14.933184523 + 14 Combine like terms: -14 + 14 = 0 0 + t = 14.933184523 + 14 t = 14.933184523 + 14 Combine like terms: 14.933184523 + 14 = 28.933184523 t = 28.933184523 Simplifying t = 28.933184523Subproblem 2
t + -14 = -14.933184523 Simplifying t + -14 = -14.933184523 Reorder the terms: -14 + t = -14.933184523 Solving -14 + t = -14.933184523 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + t = -14.933184523 + 14 Combine like terms: -14 + 14 = 0 0 + t = -14.933184523 + 14 t = -14.933184523 + 14 Combine like terms: -14.933184523 + 14 = -0.933184523 t = -0.933184523 Simplifying t = -0.933184523Solution
The solution to the problem is based on the solutions from the subproblems. t = {28.933184523, -0.933184523}
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