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Simplifying t2 + 22t + 100 = 0 Reorder the terms: 100 + 22t + t2 = 0 Solving 100 + 22t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '-100' to each side of the equation. 100 + 22t + -100 + t2 = 0 + -100 Reorder the terms: 100 + -100 + 22t + t2 = 0 + -100 Combine like terms: 100 + -100 = 0 0 + 22t + t2 = 0 + -100 22t + t2 = 0 + -100 Combine like terms: 0 + -100 = -100 22t + t2 = -100 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 = -100 + 121 Reorder the terms: 121 + 22t + t2 = -100 + 121 Combine like terms: -100 + 121 = 21 121 + 22t + t2 = 21 Factor a perfect square on the left side: (t + 11)(t + 11) = 21 Calculate the square root of the right side: 4.582575695 Break this problem into two subproblems by setting (t + 11) equal to 4.582575695 and -4.582575695.Subproblem 1
t + 11 = 4.582575695 Simplifying t + 11 = 4.582575695 Reorder the terms: 11 + t = 4.582575695 Solving 11 + t = 4.582575695 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 = 4.582575695 + -11 Combine like terms: 11 + -11 = 0 0 + t = 4.582575695 + -11 t = 4.582575695 + -11 Combine like terms: 4.582575695 + -11 = -6.417424305 t = -6.417424305 Simplifying t = -6.417424305Subproblem 2
t + 11 = -4.582575695 Simplifying t + 11 = -4.582575695 Reorder the terms: 11 + t = -4.582575695 Solving 11 + t = -4.582575695 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 = -4.582575695 + -11 Combine like terms: 11 + -11 = 0 0 + t = -4.582575695 + -11 t = -4.582575695 + -11 Combine like terms: -4.582575695 + -11 = -15.582575695 t = -15.582575695 Simplifying t = -15.582575695Solution
The solution to the problem is based on the solutions from the subproblems. t = {-6.417424305, -15.582575695}
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