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Simplifying t2 + -20t = -12 Reorder the terms: -20t + t2 = -12 Solving -20t + t2 = -12 Solving for variable 't'. Reorder the terms: 12 + -20t + t2 = -12 + 12 Combine like terms: -12 + 12 = 0 12 + -20t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + -20t + -12 + t2 = 0 + -12 Reorder the terms: 12 + -12 + -20t + t2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -20t + t2 = 0 + -12 -20t + t2 = 0 + -12 Combine like terms: 0 + -12 = -12 -20t + t2 = -12 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 = -12 + 100 Reorder the terms: 100 + -20t + t2 = -12 + 100 Combine like terms: -12 + 100 = 88 100 + -20t + t2 = 88 Factor a perfect square on the left side: (t + -10)(t + -10) = 88 Calculate the square root of the right side: 9.38083152 Break this problem into two subproblems by setting (t + -10) equal to 9.38083152 and -9.38083152.Subproblem 1
t + -10 = 9.38083152 Simplifying t + -10 = 9.38083152 Reorder the terms: -10 + t = 9.38083152 Solving -10 + t = 9.38083152 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 = 9.38083152 + 10 Combine like terms: -10 + 10 = 0 0 + t = 9.38083152 + 10 t = 9.38083152 + 10 Combine like terms: 9.38083152 + 10 = 19.38083152 t = 19.38083152 Simplifying t = 19.38083152Subproblem 2
t + -10 = -9.38083152 Simplifying t + -10 = -9.38083152 Reorder the terms: -10 + t = -9.38083152 Solving -10 + t = -9.38083152 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 = -9.38083152 + 10 Combine like terms: -10 + 10 = 0 0 + t = -9.38083152 + 10 t = -9.38083152 + 10 Combine like terms: -9.38083152 + 10 = 0.61916848 t = 0.61916848 Simplifying t = 0.61916848Solution
The solution to the problem is based on the solutions from the subproblems. t = {19.38083152, 0.61916848}
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