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Simplifying 5t2 + 12t = 1 Reorder the terms: 12t + 5t2 = 1 Solving 12t + 5t2 = 1 Solving for variable 't'. Reorder the terms: -1 + 12t + 5t2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + 12t + 5t2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.2 + 2.4t + t2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + 2.4t + 0.2 + t2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + 2.4t + t2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + 2.4t + t2 = 0 + 0.2 2.4t + t2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 2.4t + t2 = 0.2 The t term is 2.4t. Take half its coefficient (1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. 2.4t + 1.44 + t2 = 0.2 + 1.44 Reorder the terms: 1.44 + 2.4t + t2 = 0.2 + 1.44 Combine like terms: 0.2 + 1.44 = 1.64 1.44 + 2.4t + t2 = 1.64 Factor a perfect square on the left side: (t + 1.2)(t + 1.2) = 1.64 Calculate the square root of the right side: 1.280624847 Break this problem into two subproblems by setting (t + 1.2) equal to 1.280624847 and -1.280624847.Subproblem 1
t + 1.2 = 1.280624847 Simplifying t + 1.2 = 1.280624847 Reorder the terms: 1.2 + t = 1.280624847 Solving 1.2 + t = 1.280624847 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + t = 1.280624847 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + t = 1.280624847 + -1.2 t = 1.280624847 + -1.2 Combine like terms: 1.280624847 + -1.2 = 0.080624847 t = 0.080624847 Simplifying t = 0.080624847Subproblem 2
t + 1.2 = -1.280624847 Simplifying t + 1.2 = -1.280624847 Reorder the terms: 1.2 + t = -1.280624847 Solving 1.2 + t = -1.280624847 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + t = -1.280624847 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + t = -1.280624847 + -1.2 t = -1.280624847 + -1.2 Combine like terms: -1.280624847 + -1.2 = -2.480624847 t = -2.480624847 Simplifying t = -2.480624847Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.080624847, -2.480624847}
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