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Simplifying 15t2 + 150t + -315 = 0 Reorder the terms: -315 + 150t + 15t2 = 0 Solving -315 + 150t + 15t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '15'. 15(-21 + 10t + t2) = 0 Ignore the factor 15.Subproblem 1
Set the factor '(-21 + 10t + t2)' equal to zero and attempt to solve: Simplifying -21 + 10t + t2 = 0 Solving -21 + 10t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '21' to each side of the equation. -21 + 10t + 21 + t2 = 0 + 21 Reorder the terms: -21 + 21 + 10t + t2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + 10t + t2 = 0 + 21 10t + t2 = 0 + 21 Combine like terms: 0 + 21 = 21 10t + t2 = 21 The t term is 10t. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10t + 25 + t2 = 21 + 25 Reorder the terms: 25 + 10t + t2 = 21 + 25 Combine like terms: 21 + 25 = 46 25 + 10t + t2 = 46 Factor a perfect square on the left side: (t + 5)(t + 5) = 46 Calculate the square root of the right side: 6.782329983 Break this problem into two subproblems by setting (t + 5) equal to 6.782329983 and -6.782329983.Subproblem 1
t + 5 = 6.782329983 Simplifying t + 5 = 6.782329983 Reorder the terms: 5 + t = 6.782329983 Solving 5 + t = 6.782329983 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + t = 6.782329983 + -5 Combine like terms: 5 + -5 = 0 0 + t = 6.782329983 + -5 t = 6.782329983 + -5 Combine like terms: 6.782329983 + -5 = 1.782329983 t = 1.782329983 Simplifying t = 1.782329983Subproblem 2
t + 5 = -6.782329983 Simplifying t + 5 = -6.782329983 Reorder the terms: 5 + t = -6.782329983 Solving 5 + t = -6.782329983 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + t = -6.782329983 + -5 Combine like terms: 5 + -5 = 0 0 + t = -6.782329983 + -5 t = -6.782329983 + -5 Combine like terms: -6.782329983 + -5 = -11.782329983 t = -11.782329983 Simplifying t = -11.782329983Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.782329983, -11.782329983}Solution
t = {1.782329983, -11.782329983}
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