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Simplifying t2 + 22t + -5 = 0 Reorder the terms: -5 + 22t + t2 = 0 Solving -5 + 22t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + 22t + 5 + t2 = 0 + 5 Reorder the terms: -5 + 5 + 22t + t2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 22t + t2 = 0 + 5 22t + t2 = 0 + 5 Combine like terms: 0 + 5 = 5 22t + t2 = 5 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 = 5 + 121 Reorder the terms: 121 + 22t + t2 = 5 + 121 Combine like terms: 5 + 121 = 126 121 + 22t + t2 = 126 Factor a perfect square on the left side: (t + 11)(t + 11) = 126 Calculate the square root of the right side: 11.22497216 Break this problem into two subproblems by setting (t + 11) equal to 11.22497216 and -11.22497216.Subproblem 1
t + 11 = 11.22497216 Simplifying t + 11 = 11.22497216 Reorder the terms: 11 + t = 11.22497216 Solving 11 + t = 11.22497216 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 = 11.22497216 + -11 Combine like terms: 11 + -11 = 0 0 + t = 11.22497216 + -11 t = 11.22497216 + -11 Combine like terms: 11.22497216 + -11 = 0.22497216 t = 0.22497216 Simplifying t = 0.22497216Subproblem 2
t + 11 = -11.22497216 Simplifying t + 11 = -11.22497216 Reorder the terms: 11 + t = -11.22497216 Solving 11 + t = -11.22497216 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 = -11.22497216 + -11 Combine like terms: 11 + -11 = 0 0 + t = -11.22497216 + -11 t = -11.22497216 + -11 Combine like terms: -11.22497216 + -11 = -22.22497216 t = -22.22497216 Simplifying t = -22.22497216Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.22497216, -22.22497216}
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