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Simplifying t2 + -10t + 21 = 1 Reorder the terms: 21 + -10t + t2 = 1 Solving 21 + -10t + t2 = 1 Solving for variable 't'. Reorder the terms: 21 + -1 + -10t + t2 = 1 + -1 Combine like terms: 21 + -1 = 20 20 + -10t + t2 = 1 + -1 Combine like terms: 1 + -1 = 0 20 + -10t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-20' to each side of the equation. 20 + -10t + -20 + t2 = 0 + -20 Reorder the terms: 20 + -20 + -10t + t2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -10t + t2 = 0 + -20 -10t + t2 = 0 + -20 Combine like terms: 0 + -20 = -20 -10t + t2 = -20 The t term is -10t. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10t + 25 + t2 = -20 + 25 Reorder the terms: 25 + -10t + t2 = -20 + 25 Combine like terms: -20 + 25 = 5 25 + -10t + t2 = 5 Factor a perfect square on the left side: (t + -5)(t + -5) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (t + -5) equal to 2.236067978 and -2.236067978.Subproblem 1
t + -5 = 2.236067978 Simplifying t + -5 = 2.236067978 Reorder the terms: -5 + t = 2.236067978 Solving -5 + t = 2.236067978 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + t = 2.236067978 + 5 Combine like terms: -5 + 5 = 0 0 + t = 2.236067978 + 5 t = 2.236067978 + 5 Combine like terms: 2.236067978 + 5 = 7.236067978 t = 7.236067978 Simplifying t = 7.236067978Subproblem 2
t + -5 = -2.236067978 Simplifying t + -5 = -2.236067978 Reorder the terms: -5 + t = -2.236067978 Solving -5 + t = -2.236067978 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + t = -2.236067978 + 5 Combine like terms: -5 + 5 = 0 0 + t = -2.236067978 + 5 t = -2.236067978 + 5 Combine like terms: -2.236067978 + 5 = 2.763932022 t = 2.763932022 Simplifying t = 2.763932022Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.236067978, 2.763932022}
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