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Simplifying t2 + 20t + -3200 = 0 Reorder the terms: -3200 + 20t + t2 = 0 Solving -3200 + 20t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '3200' to each side of the equation. -3200 + 20t + 3200 + t2 = 0 + 3200 Reorder the terms: -3200 + 3200 + 20t + t2 = 0 + 3200 Combine like terms: -3200 + 3200 = 0 0 + 20t + t2 = 0 + 3200 20t + t2 = 0 + 3200 Combine like terms: 0 + 3200 = 3200 20t + t2 = 3200 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 = 3200 + 100 Reorder the terms: 100 + 20t + t2 = 3200 + 100 Combine like terms: 3200 + 100 = 3300 100 + 20t + t2 = 3300 Factor a perfect square on the left side: (t + 10)(t + 10) = 3300 Calculate the square root of the right side: 57.445626465 Break this problem into two subproblems by setting (t + 10) equal to 57.445626465 and -57.445626465.Subproblem 1
t + 10 = 57.445626465 Simplifying t + 10 = 57.445626465 Reorder the terms: 10 + t = 57.445626465 Solving 10 + t = 57.445626465 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 = 57.445626465 + -10 Combine like terms: 10 + -10 = 0 0 + t = 57.445626465 + -10 t = 57.445626465 + -10 Combine like terms: 57.445626465 + -10 = 47.445626465 t = 47.445626465 Simplifying t = 47.445626465Subproblem 2
t + 10 = -57.445626465 Simplifying t + 10 = -57.445626465 Reorder the terms: 10 + t = -57.445626465 Solving 10 + t = -57.445626465 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 = -57.445626465 + -10 Combine like terms: 10 + -10 = 0 0 + t = -57.445626465 + -10 t = -57.445626465 + -10 Combine like terms: -57.445626465 + -10 = -67.445626465 t = -67.445626465 Simplifying t = -67.445626465Solution
The solution to the problem is based on the solutions from the subproblems. t = {47.445626465, -67.445626465}
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