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Simplifying t5 + -15t4 + -56t3 = 0 Reorder the terms: -56t3 + -15t4 + t5 = 0 Solving -56t3 + -15t4 + t5 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), 't3'. t3(-56 + -15t + t2) = 0Subproblem 1
Set the factor 't3' equal to zero and attempt to solve: Simplifying t3 = 0 Solving t3 = 0 Move all terms containing t to the left, all other terms to the right. Simplifying t3 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-56 + -15t + t2)' equal to zero and attempt to solve: Simplifying -56 + -15t + t2 = 0 Solving -56 + -15t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '56' to each side of the equation. -56 + -15t + 56 + t2 = 0 + 56 Reorder the terms: -56 + 56 + -15t + t2 = 0 + 56 Combine like terms: -56 + 56 = 0 0 + -15t + t2 = 0 + 56 -15t + t2 = 0 + 56 Combine like terms: 0 + 56 = 56 -15t + t2 = 56 The t term is -15t. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15t + 56.25 + t2 = 56 + 56.25 Reorder the terms: 56.25 + -15t + t2 = 56 + 56.25 Combine like terms: 56 + 56.25 = 112.25 56.25 + -15t + t2 = 112.25 Factor a perfect square on the left side: (t + -7.5)(t + -7.5) = 112.25 Calculate the square root of the right side: 10.59481005 Break this problem into two subproblems by setting (t + -7.5) equal to 10.59481005 and -10.59481005.Subproblem 1
t + -7.5 = 10.59481005 Simplifying t + -7.5 = 10.59481005 Reorder the terms: -7.5 + t = 10.59481005 Solving -7.5 + t = 10.59481005 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + t = 10.59481005 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + t = 10.59481005 + 7.5 t = 10.59481005 + 7.5 Combine like terms: 10.59481005 + 7.5 = 18.09481005 t = 18.09481005 Simplifying t = 18.09481005Subproblem 2
t + -7.5 = -10.59481005 Simplifying t + -7.5 = -10.59481005 Reorder the terms: -7.5 + t = -10.59481005 Solving -7.5 + t = -10.59481005 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + t = -10.59481005 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + t = -10.59481005 + 7.5 t = -10.59481005 + 7.5 Combine like terms: -10.59481005 + 7.5 = -3.09481005 t = -3.09481005 Simplifying t = -3.09481005Solution
The solution to the problem is based on the solutions from the subproblems. t = {18.09481005, -3.09481005}Solution
t = {18.09481005, -3.09481005}
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