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Simplifying t4 + -3t3 + -20t2 = 0 Reorder the terms: -20t2 + -3t3 + t4 = 0 Solving -20t2 + -3t3 + t4 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), 't2'. t2(-20 + -3t + t2) = 0Subproblem 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 '(-20 + -3t + t2)' equal to zero and attempt to solve: Simplifying -20 + -3t + t2 = 0 Solving -20 + -3t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '20' to each side of the equation. -20 + -3t + 20 + t2 = 0 + 20 Reorder the terms: -20 + 20 + -3t + t2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -3t + t2 = 0 + 20 -3t + t2 = 0 + 20 Combine like terms: 0 + 20 = 20 -3t + t2 = 20 The t term is -3t. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3t + 2.25 + t2 = 20 + 2.25 Reorder the terms: 2.25 + -3t + t2 = 20 + 2.25 Combine like terms: 20 + 2.25 = 22.25 2.25 + -3t + t2 = 22.25 Factor a perfect square on the left side: (t + -1.5)(t + -1.5) = 22.25 Calculate the square root of the right side: 4.716990566 Break this problem into two subproblems by setting (t + -1.5) equal to 4.716990566 and -4.716990566.Subproblem 1
t + -1.5 = 4.716990566 Simplifying t + -1.5 = 4.716990566 Reorder the terms: -1.5 + t = 4.716990566 Solving -1.5 + t = 4.716990566 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + t = 4.716990566 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + t = 4.716990566 + 1.5 t = 4.716990566 + 1.5 Combine like terms: 4.716990566 + 1.5 = 6.216990566 t = 6.216990566 Simplifying t = 6.216990566Subproblem 2
t + -1.5 = -4.716990566 Simplifying t + -1.5 = -4.716990566 Reorder the terms: -1.5 + t = -4.716990566 Solving -1.5 + t = -4.716990566 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + t = -4.716990566 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + t = -4.716990566 + 1.5 t = -4.716990566 + 1.5 Combine like terms: -4.716990566 + 1.5 = -3.216990566 t = -3.216990566 Simplifying t = -3.216990566Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.216990566, -3.216990566}Solution
t = {0, 6.216990566, -3.216990566}
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