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Simplifying t2 + 40t + 80 = 0 Reorder the terms: 80 + 40t + t2 = 0 Solving 80 + 40t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '-80' to each side of the equation. 80 + 40t + -80 + t2 = 0 + -80 Reorder the terms: 80 + -80 + 40t + t2 = 0 + -80 Combine like terms: 80 + -80 = 0 0 + 40t + t2 = 0 + -80 40t + t2 = 0 + -80 Combine like terms: 0 + -80 = -80 40t + t2 = -80 The t term is 40t. Take half its coefficient (20). Square it (400) and add it to both sides. Add '400' to each side of the equation. 40t + 400 + t2 = -80 + 400 Reorder the terms: 400 + 40t + t2 = -80 + 400 Combine like terms: -80 + 400 = 320 400 + 40t + t2 = 320 Factor a perfect square on the left side: (t + 20)(t + 20) = 320 Calculate the square root of the right side: 17.88854382 Break this problem into two subproblems by setting (t + 20) equal to 17.88854382 and -17.88854382.Subproblem 1
t + 20 = 17.88854382 Simplifying t + 20 = 17.88854382 Reorder the terms: 20 + t = 17.88854382 Solving 20 + t = 17.88854382 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + t = 17.88854382 + -20 Combine like terms: 20 + -20 = 0 0 + t = 17.88854382 + -20 t = 17.88854382 + -20 Combine like terms: 17.88854382 + -20 = -2.11145618 t = -2.11145618 Simplifying t = -2.11145618Subproblem 2
t + 20 = -17.88854382 Simplifying t + 20 = -17.88854382 Reorder the terms: 20 + t = -17.88854382 Solving 20 + t = -17.88854382 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + t = -17.88854382 + -20 Combine like terms: 20 + -20 = 0 0 + t = -17.88854382 + -20 t = -17.88854382 + -20 Combine like terms: -17.88854382 + -20 = -37.88854382 t = -37.88854382 Simplifying t = -37.88854382Solution
The solution to the problem is based on the solutions from the subproblems. t = {-2.11145618, -37.88854382}
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