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Simplifying t(t2 + -1t + -24) = 0 Reorder the terms: t(-24 + -1t + t2) = 0 (-24 * t + -1t * t + t2 * t) = 0 (-24t + -1t2 + t3) = 0 Solving -24t + -1t2 + t3 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), 't'. t(-24 + -1t + 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 '(-24 + -1t + t2)' equal to zero and attempt to solve: Simplifying -24 + -1t + t2 = 0 Solving -24 + -1t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '24' to each side of the equation. -24 + -1t + 24 + t2 = 0 + 24 Reorder the terms: -24 + 24 + -1t + t2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -1t + t2 = 0 + 24 -1t + t2 = 0 + 24 Combine like terms: 0 + 24 = 24 -1t + t2 = 24 The t term is -1t. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1t + 0.25 + t2 = 24 + 0.25 Reorder the terms: 0.25 + -1t + t2 = 24 + 0.25 Combine like terms: 24 + 0.25 = 24.25 0.25 + -1t + t2 = 24.25 Factor a perfect square on the left side: (t + -0.5)(t + -0.5) = 24.25 Calculate the square root of the right side: 4.924428901 Break this problem into two subproblems by setting (t + -0.5) equal to 4.924428901 and -4.924428901.Subproblem 1
t + -0.5 = 4.924428901 Simplifying t + -0.5 = 4.924428901 Reorder the terms: -0.5 + t = 4.924428901 Solving -0.5 + t = 4.924428901 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + t = 4.924428901 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + t = 4.924428901 + 0.5 t = 4.924428901 + 0.5 Combine like terms: 4.924428901 + 0.5 = 5.424428901 t = 5.424428901 Simplifying t = 5.424428901Subproblem 2
t + -0.5 = -4.924428901 Simplifying t + -0.5 = -4.924428901 Reorder the terms: -0.5 + t = -4.924428901 Solving -0.5 + t = -4.924428901 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + t = -4.924428901 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + t = -4.924428901 + 0.5 t = -4.924428901 + 0.5 Combine like terms: -4.924428901 + 0.5 = -4.424428901 t = -4.424428901 Simplifying t = -4.424428901Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.424428901, -4.424428901}Solution
t = {0, 5.424428901, -4.424428901}
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