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Simplifying t2 + -8t + -20 = 20 Reorder the terms: -20 + -8t + t2 = 20 Solving -20 + -8t + t2 = 20 Solving for variable 't'. Reorder the terms: -20 + -20 + -8t + t2 = 20 + -20 Combine like terms: -20 + -20 = -40 -40 + -8t + t2 = 20 + -20 Combine like terms: 20 + -20 = 0 -40 + -8t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '40' to each side of the equation. -40 + -8t + 40 + t2 = 0 + 40 Reorder the terms: -40 + 40 + -8t + t2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + -8t + t2 = 0 + 40 -8t + t2 = 0 + 40 Combine like terms: 0 + 40 = 40 -8t + t2 = 40 The t term is -8t. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8t + 16 + t2 = 40 + 16 Reorder the terms: 16 + -8t + t2 = 40 + 16 Combine like terms: 40 + 16 = 56 16 + -8t + t2 = 56 Factor a perfect square on the left side: (t + -4)(t + -4) = 56 Calculate the square root of the right side: 7.483314774 Break this problem into two subproblems by setting (t + -4) equal to 7.483314774 and -7.483314774.Subproblem 1
t + -4 = 7.483314774 Simplifying t + -4 = 7.483314774 Reorder the terms: -4 + t = 7.483314774 Solving -4 + t = 7.483314774 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = 7.483314774 + 4 Combine like terms: -4 + 4 = 0 0 + t = 7.483314774 + 4 t = 7.483314774 + 4 Combine like terms: 7.483314774 + 4 = 11.483314774 t = 11.483314774 Simplifying t = 11.483314774Subproblem 2
t + -4 = -7.483314774 Simplifying t + -4 = -7.483314774 Reorder the terms: -4 + t = -7.483314774 Solving -4 + t = -7.483314774 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = -7.483314774 + 4 Combine like terms: -4 + 4 = 0 0 + t = -7.483314774 + 4 t = -7.483314774 + 4 Combine like terms: -7.483314774 + 4 = -3.483314774 t = -3.483314774 Simplifying t = -3.483314774Solution
The solution to the problem is based on the solutions from the subproblems. t = {11.483314774, -3.483314774}
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