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Simplifying t2 + 22t + 94 = 0 Reorder the terms: 94 + 22t + t2 = 0 Solving 94 + 22t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '-94' to each side of the equation. 94 + 22t + -94 + t2 = 0 + -94 Reorder the terms: 94 + -94 + 22t + t2 = 0 + -94 Combine like terms: 94 + -94 = 0 0 + 22t + t2 = 0 + -94 22t + t2 = 0 + -94 Combine like terms: 0 + -94 = -94 22t + t2 = -94 The t term is 22t. Take half its coefficient (11). Square it (121) and add it to both sides. Add '121' to each side of the equation. 22t + 121 + t2 = -94 + 121 Reorder the terms: 121 + 22t + t2 = -94 + 121 Combine like terms: -94 + 121 = 27 121 + 22t + t2 = 27 Factor a perfect square on the left side: (t + 11)(t + 11) = 27 Calculate the square root of the right side: 5.196152423 Break this problem into two subproblems by setting (t + 11) equal to 5.196152423 and -5.196152423.Subproblem 1
t + 11 = 5.196152423 Simplifying t + 11 = 5.196152423 Reorder the terms: 11 + t = 5.196152423 Solving 11 + t = 5.196152423 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + t = 5.196152423 + -11 Combine like terms: 11 + -11 = 0 0 + t = 5.196152423 + -11 t = 5.196152423 + -11 Combine like terms: 5.196152423 + -11 = -5.803847577 t = -5.803847577 Simplifying t = -5.803847577Subproblem 2
t + 11 = -5.196152423 Simplifying t + 11 = -5.196152423 Reorder the terms: 11 + t = -5.196152423 Solving 11 + t = -5.196152423 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + t = -5.196152423 + -11 Combine like terms: 11 + -11 = 0 0 + t = -5.196152423 + -11 t = -5.196152423 + -11 Combine like terms: -5.196152423 + -11 = -16.196152423 t = -16.196152423 Simplifying t = -16.196152423Solution
The solution to the problem is based on the solutions from the subproblems. t = {-5.803847577, -16.196152423}
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