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Simplifying 5t2 + 30t + 35 = 0 Reorder the terms: 35 + 30t + 5t2 = 0 Solving 35 + 30t + 5t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '5'. 5(7 + 6t + t2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(7 + 6t + t2)' equal to zero and attempt to solve: Simplifying 7 + 6t + t2 = 0 Solving 7 + 6t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + 6t + -7 + t2 = 0 + -7 Reorder the terms: 7 + -7 + 6t + t2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 6t + t2 = 0 + -7 6t + t2 = 0 + -7 Combine like terms: 0 + -7 = -7 6t + t2 = -7 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 = -7 + 9 Reorder the terms: 9 + 6t + t2 = -7 + 9 Combine like terms: -7 + 9 = 2 9 + 6t + t2 = 2 Factor a perfect square on the left side: (t + 3)(t + 3) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (t + 3) equal to 1.414213562 and -1.414213562.Subproblem 1
t + 3 = 1.414213562 Simplifying t + 3 = 1.414213562 Reorder the terms: 3 + t = 1.414213562 Solving 3 + t = 1.414213562 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 = 1.414213562 + -3 Combine like terms: 3 + -3 = 0 0 + t = 1.414213562 + -3 t = 1.414213562 + -3 Combine like terms: 1.414213562 + -3 = -1.585786438 t = -1.585786438 Simplifying t = -1.585786438Subproblem 2
t + 3 = -1.414213562 Simplifying t + 3 = -1.414213562 Reorder the terms: 3 + t = -1.414213562 Solving 3 + t = -1.414213562 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 = -1.414213562 + -3 Combine like terms: 3 + -3 = 0 0 + t = -1.414213562 + -3 t = -1.414213562 + -3 Combine like terms: -1.414213562 + -3 = -4.414213562 t = -4.414213562 Simplifying t = -4.414213562Solution
The solution to the problem is based on the solutions from the subproblems. t = {-1.585786438, -4.414213562}Solution
t = {-1.585786438, -4.414213562}
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