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Simplifying 7t2 + t + -0.25 = 0 Reorder the terms: -0.25 + t + 7t2 = 0 Solving -0.25 + t + 7t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.03571428571 + 0.1428571429t + t2 = 0 Move the constant term to the right: Add '0.03571428571' to each side of the equation. -0.03571428571 + 0.1428571429t + 0.03571428571 + t2 = 0 + 0.03571428571 Reorder the terms: -0.03571428571 + 0.03571428571 + 0.1428571429t + t2 = 0 + 0.03571428571 Combine like terms: -0.03571428571 + 0.03571428571 = 0.00000000000 0.00000000000 + 0.1428571429t + t2 = 0 + 0.03571428571 0.1428571429t + t2 = 0 + 0.03571428571 Combine like terms: 0 + 0.03571428571 = 0.03571428571 0.1428571429t + t2 = 0.03571428571 The t term is t. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.1428571429t + 0.25 + t2 = 0.03571428571 + 0.25 Reorder the terms: 0.25 + 0.1428571429t + t2 = 0.03571428571 + 0.25 Combine like terms: 0.03571428571 + 0.25 = 0.28571428571 0.25 + 0.1428571429t + t2 = 0.28571428571 Factor a perfect square on the left side: (t + 0.5)(t + 0.5) = 0.28571428571 Calculate the square root of the right side: 0.534522484 Break this problem into two subproblems by setting (t + 0.5) equal to 0.534522484 and -0.534522484.Subproblem 1
t + 0.5 = 0.534522484 Simplifying t + 0.5 = 0.534522484 Reorder the terms: 0.5 + t = 0.534522484 Solving 0.5 + t = 0.534522484 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + t = 0.534522484 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = 0.534522484 + -0.5 t = 0.534522484 + -0.5 Combine like terms: 0.534522484 + -0.5 = 0.034522484 t = 0.034522484 Simplifying t = 0.034522484Subproblem 2
t + 0.5 = -0.534522484 Simplifying t + 0.5 = -0.534522484 Reorder the terms: 0.5 + t = -0.534522484 Solving 0.5 + t = -0.534522484 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + t = -0.534522484 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = -0.534522484 + -0.5 t = -0.534522484 + -0.5 Combine like terms: -0.534522484 + -0.5 = -1.034522484 t = -1.034522484 Simplifying t = -1.034522484Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.034522484, -1.034522484}
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