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Simplifying t3 + -9t2 + 15t = 0 Reorder the terms: 15t + -9t2 + t3 = 0 Solving 15t + -9t2 + t3 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), 't'. t(15 + -9t + t2) = 0Subproblem 1
Set the factor 't' equal to zero and attempt to solve: Simplifying t = 0 Solving t = 0 Move all terms containing t to the left, all other terms to the right. Simplifying t = 0Subproblem 2
Set the factor '(15 + -9t + t2)' equal to zero and attempt to solve: Simplifying 15 + -9t + t2 = 0 Solving 15 + -9t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-15' to each side of the equation. 15 + -9t + -15 + t2 = 0 + -15 Reorder the terms: 15 + -15 + -9t + t2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -9t + t2 = 0 + -15 -9t + t2 = 0 + -15 Combine like terms: 0 + -15 = -15 -9t + t2 = -15 The t term is -9t. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9t + 20.25 + t2 = -15 + 20.25 Reorder the terms: 20.25 + -9t + t2 = -15 + 20.25 Combine like terms: -15 + 20.25 = 5.25 20.25 + -9t + t2 = 5.25 Factor a perfect square on the left side: (t + -4.5)(t + -4.5) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (t + -4.5) equal to 2.291287847 and -2.291287847.Subproblem 1
t + -4.5 = 2.291287847 Simplifying t + -4.5 = 2.291287847 Reorder the terms: -4.5 + t = 2.291287847 Solving -4.5 + t = 2.291287847 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + t = 2.291287847 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + t = 2.291287847 + 4.5 t = 2.291287847 + 4.5 Combine like terms: 2.291287847 + 4.5 = 6.791287847 t = 6.791287847 Simplifying t = 6.791287847Subproblem 2
t + -4.5 = -2.291287847 Simplifying t + -4.5 = -2.291287847 Reorder the terms: -4.5 + t = -2.291287847 Solving -4.5 + t = -2.291287847 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + t = -2.291287847 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + t = -2.291287847 + 4.5 t = -2.291287847 + 4.5 Combine like terms: -2.291287847 + 4.5 = 2.208712153 t = 2.208712153 Simplifying t = 2.208712153Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.791287847, 2.208712153}Solution
t = {0, 6.791287847, 2.208712153}
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