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Simplifying 4t2 + 24t + 13 = 0 Reorder the terms: 13 + 24t + 4t2 = 0 Solving 13 + 24t + 4t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 3.25 + 6t + t2 = 0 Move the constant term to the right: Add '-3.25' to each side of the equation. 3.25 + 6t + -3.25 + t2 = 0 + -3.25 Reorder the terms: 3.25 + -3.25 + 6t + t2 = 0 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + 6t + t2 = 0 + -3.25 6t + t2 = 0 + -3.25 Combine like terms: 0 + -3.25 = -3.25 6t + t2 = -3.25 The t term is 6t. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6t + 9 + t2 = -3.25 + 9 Reorder the terms: 9 + 6t + t2 = -3.25 + 9 Combine like terms: -3.25 + 9 = 5.75 9 + 6t + t2 = 5.75 Factor a perfect square on the left side: (t + 3)(t + 3) = 5.75 Calculate the square root of the right side: 2.397915762 Break this problem into two subproblems by setting (t + 3) equal to 2.397915762 and -2.397915762.Subproblem 1
t + 3 = 2.397915762 Simplifying t + 3 = 2.397915762 Reorder the terms: 3 + t = 2.397915762 Solving 3 + t = 2.397915762 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + t = 2.397915762 + -3 Combine like terms: 3 + -3 = 0 0 + t = 2.397915762 + -3 t = 2.397915762 + -3 Combine like terms: 2.397915762 + -3 = -0.602084238 t = -0.602084238 Simplifying t = -0.602084238Subproblem 2
t + 3 = -2.397915762 Simplifying t + 3 = -2.397915762 Reorder the terms: 3 + t = -2.397915762 Solving 3 + t = -2.397915762 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + t = -2.397915762 + -3 Combine like terms: 3 + -3 = 0 0 + t = -2.397915762 + -3 t = -2.397915762 + -3 Combine like terms: -2.397915762 + -3 = -5.397915762 t = -5.397915762 Simplifying t = -5.397915762Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.602084238, -5.397915762}
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