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Simplifying 4t2 + -24t + -24 = 0 Reorder the terms: -24 + -24t + 4t2 = 0 Solving -24 + -24t + 4t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4'. 4(-6 + -6t + t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-6 + -6t + t2)' equal to zero and attempt to solve: Simplifying -6 + -6t + t2 = 0 Solving -6 + -6t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + -6t + 6 + t2 = 0 + 6 Reorder the terms: -6 + 6 + -6t + t2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -6t + t2 = 0 + 6 -6t + t2 = 0 + 6 Combine like terms: 0 + 6 = 6 -6t + t2 = 6 The t term is -6t. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6t + 9 + t2 = 6 + 9 Reorder the terms: 9 + -6t + t2 = 6 + 9 Combine like terms: 6 + 9 = 15 9 + -6t + t2 = 15 Factor a perfect square on the left side: (t + -3)(t + -3) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (t + -3) equal to 3.872983346 and -3.872983346.Subproblem 1
t + -3 = 3.872983346 Simplifying t + -3 = 3.872983346 Reorder the terms: -3 + t = 3.872983346 Solving -3 + t = 3.872983346 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = 3.872983346 + 3 Combine like terms: -3 + 3 = 0 0 + t = 3.872983346 + 3 t = 3.872983346 + 3 Combine like terms: 3.872983346 + 3 = 6.872983346 t = 6.872983346 Simplifying t = 6.872983346Subproblem 2
t + -3 = -3.872983346 Simplifying t + -3 = -3.872983346 Reorder the terms: -3 + t = -3.872983346 Solving -3 + t = -3.872983346 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = -3.872983346 + 3 Combine like terms: -3 + 3 = 0 0 + t = -3.872983346 + 3 t = -3.872983346 + 3 Combine like terms: -3.872983346 + 3 = -0.872983346 t = -0.872983346 Simplifying t = -0.872983346Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.872983346, -0.872983346}Solution
t = {6.872983346, -0.872983346}
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