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Simplifying 3(t2 + -4t) = 24 Reorder the terms: 3(-4t + t2) = 24 (-4t * 3 + t2 * 3) = 24 (-12t + 3t2) = 24 Solving -12t + 3t2 = 24 Solving for variable 't'. Reorder the terms: -24 + -12t + 3t2 = 24 + -24 Combine like terms: 24 + -24 = 0 -24 + -12t + 3t2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-8 + -4t + t2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-8 + -4t + t2)' equal to zero and attempt to solve: Simplifying -8 + -4t + t2 = 0 Solving -8 + -4t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + -4t + 8 + t2 = 0 + 8 Reorder the terms: -8 + 8 + -4t + t2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -4t + t2 = 0 + 8 -4t + t2 = 0 + 8 Combine like terms: 0 + 8 = 8 -4t + t2 = 8 The t term is -4t. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4t + 4 + t2 = 8 + 4 Reorder the terms: 4 + -4t + t2 = 8 + 4 Combine like terms: 8 + 4 = 12 4 + -4t + t2 = 12 Factor a perfect square on the left side: (t + -2)(t + -2) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (t + -2) equal to 3.464101615 and -3.464101615.Subproblem 1
t + -2 = 3.464101615 Simplifying t + -2 = 3.464101615 Reorder the terms: -2 + t = 3.464101615 Solving -2 + t = 3.464101615 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = 3.464101615 + 2 Combine like terms: -2 + 2 = 0 0 + t = 3.464101615 + 2 t = 3.464101615 + 2 Combine like terms: 3.464101615 + 2 = 5.464101615 t = 5.464101615 Simplifying t = 5.464101615Subproblem 2
t + -2 = -3.464101615 Simplifying t + -2 = -3.464101615 Reorder the terms: -2 + t = -3.464101615 Solving -2 + t = -3.464101615 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = -3.464101615 + 2 Combine like terms: -2 + 2 = 0 0 + t = -3.464101615 + 2 t = -3.464101615 + 2 Combine like terms: -3.464101615 + 2 = -1.464101615 t = -1.464101615 Simplifying t = -1.464101615Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.464101615, -1.464101615}Solution
t = {5.464101615, -1.464101615}
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