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Simplifying 9t2(2t + -6 + 5t2) = 0 Reorder the terms: 9t2(-6 + 2t + 5t2) = 0 (-6 * 9t2 + 2t * 9t2 + 5t2 * 9t2) = 0 (-54t2 + 18t3 + 45t4) = 0 Solving -54t2 + 18t3 + 45t4 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '9t2'. 9t2(-6 + 2t + 5t2) = 0 Ignore the factor 9.Subproblem 1
Set the factor 't2' equal to zero and attempt to solve: Simplifying t2 = 0 Solving t2 = 0 Move all terms containing t to the left, all other terms to the right. Simplifying t2 = 0 Take the square root of each side: t = {0}Subproblem 2
Set the factor '(-6 + 2t + 5t2)' equal to zero and attempt to solve: Simplifying -6 + 2t + 5t2 = 0 Solving -6 + 2t + 5t2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.2 + 0.4t + t2 = 0 Move the constant term to the right: Add '1.2' to each side of the equation. -1.2 + 0.4t + 1.2 + t2 = 0 + 1.2 Reorder the terms: -1.2 + 1.2 + 0.4t + t2 = 0 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + 0.4t + t2 = 0 + 1.2 0.4t + t2 = 0 + 1.2 Combine like terms: 0 + 1.2 = 1.2 0.4t + t2 = 1.2 The t term is 0.4t. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4t + 0.04 + t2 = 1.2 + 0.04 Reorder the terms: 0.04 + 0.4t + t2 = 1.2 + 0.04 Combine like terms: 1.2 + 0.04 = 1.24 0.04 + 0.4t + t2 = 1.24 Factor a perfect square on the left side: (t + 0.2)(t + 0.2) = 1.24 Calculate the square root of the right side: 1.113552873 Break this problem into two subproblems by setting (t + 0.2) equal to 1.113552873 and -1.113552873.Subproblem 1
t + 0.2 = 1.113552873 Simplifying t + 0.2 = 1.113552873 Reorder the terms: 0.2 + t = 1.113552873 Solving 0.2 + t = 1.113552873 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + t = 1.113552873 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + t = 1.113552873 + -0.2 t = 1.113552873 + -0.2 Combine like terms: 1.113552873 + -0.2 = 0.913552873 t = 0.913552873 Simplifying t = 0.913552873Subproblem 2
t + 0.2 = -1.113552873 Simplifying t + 0.2 = -1.113552873 Reorder the terms: 0.2 + t = -1.113552873 Solving 0.2 + t = -1.113552873 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + t = -1.113552873 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + t = -1.113552873 + -0.2 t = -1.113552873 + -0.2 Combine like terms: -1.113552873 + -0.2 = -1.313552873 t = -1.313552873 Simplifying t = -1.313552873Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.913552873, -1.313552873}Solution
t = {0, 0.913552873, -1.313552873}
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