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Simplifying -15(t2 + 10t + 5) = 0 Reorder the terms: -15(5 + 10t + t2) = 0 (5 * -15 + 10t * -15 + t2 * -15) = 0 (-75 + -150t + -15t2) = 0 Solving -75 + -150t + -15t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '-15'. -15(5 + 10t + t2) = 0 Ignore the factor -15.Subproblem 1
Set the factor '(5 + 10t + t2)' equal to zero and attempt to solve: Simplifying 5 + 10t + t2 = 0 Solving 5 + 10t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + 10t + -5 + t2 = 0 + -5 Reorder the terms: 5 + -5 + 10t + t2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 10t + t2 = 0 + -5 10t + t2 = 0 + -5 Combine like terms: 0 + -5 = -5 10t + t2 = -5 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 = -5 + 25 Reorder the terms: 25 + 10t + t2 = -5 + 25 Combine like terms: -5 + 25 = 20 25 + 10t + t2 = 20 Factor a perfect square on the left side: (t + 5)(t + 5) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (t + 5) equal to 4.472135955 and -4.472135955.Subproblem 1
t + 5 = 4.472135955 Simplifying t + 5 = 4.472135955 Reorder the terms: 5 + t = 4.472135955 Solving 5 + t = 4.472135955 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 = 4.472135955 + -5 Combine like terms: 5 + -5 = 0 0 + t = 4.472135955 + -5 t = 4.472135955 + -5 Combine like terms: 4.472135955 + -5 = -0.527864045 t = -0.527864045 Simplifying t = -0.527864045Subproblem 2
t + 5 = -4.472135955 Simplifying t + 5 = -4.472135955 Reorder the terms: 5 + t = -4.472135955 Solving 5 + t = -4.472135955 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 = -4.472135955 + -5 Combine like terms: 5 + -5 = 0 0 + t = -4.472135955 + -5 t = -4.472135955 + -5 Combine like terms: -4.472135955 + -5 = -9.472135955 t = -9.472135955 Simplifying t = -9.472135955Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.527864045, -9.472135955}Solution
t = {-0.527864045, -9.472135955}
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