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Simplifying t2 + -20t + -60 = 0 Reorder the terms: -60 + -20t + t2 = 0 Solving -60 + -20t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '60' to each side of the equation. -60 + -20t + 60 + t2 = 0 + 60 Reorder the terms: -60 + 60 + -20t + t2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + -20t + t2 = 0 + 60 -20t + t2 = 0 + 60 Combine like terms: 0 + 60 = 60 -20t + t2 = 60 The t term is -20t. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20t + 100 + t2 = 60 + 100 Reorder the terms: 100 + -20t + t2 = 60 + 100 Combine like terms: 60 + 100 = 160 100 + -20t + t2 = 160 Factor a perfect square on the left side: (t + -10)(t + -10) = 160 Calculate the square root of the right side: 12.649110641 Break this problem into two subproblems by setting (t + -10) equal to 12.649110641 and -12.649110641.Subproblem 1
t + -10 = 12.649110641 Simplifying t + -10 = 12.649110641 Reorder the terms: -10 + t = 12.649110641 Solving -10 + t = 12.649110641 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + t = 12.649110641 + 10 Combine like terms: -10 + 10 = 0 0 + t = 12.649110641 + 10 t = 12.649110641 + 10 Combine like terms: 12.649110641 + 10 = 22.649110641 t = 22.649110641 Simplifying t = 22.649110641Subproblem 2
t + -10 = -12.649110641 Simplifying t + -10 = -12.649110641 Reorder the terms: -10 + t = -12.649110641 Solving -10 + t = -12.649110641 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + t = -12.649110641 + 10 Combine like terms: -10 + 10 = 0 0 + t = -12.649110641 + 10 t = -12.649110641 + 10 Combine like terms: -12.649110641 + 10 = -2.649110641 t = -2.649110641 Simplifying t = -2.649110641Solution
The solution to the problem is based on the solutions from the subproblems. t = {22.649110641, -2.649110641}
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