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Simplifying 0 = -3t2 + 18t + 12 Reorder the terms: 0 = 12 + 18t + -3t2 Solving 0 = 12 + 18t + -3t2 Solving for variable 't'. Combine like terms: 0 + -12 = -12 -12 + -18t + 3t2 = 12 + 18t + -3t2 + -12 + -18t + 3t2 Reorder the terms: -12 + -18t + 3t2 = 12 + -12 + 18t + -18t + -3t2 + 3t2 Combine like terms: 12 + -12 = 0 -12 + -18t + 3t2 = 0 + 18t + -18t + -3t2 + 3t2 -12 + -18t + 3t2 = 18t + -18t + -3t2 + 3t2 Combine like terms: 18t + -18t = 0 -12 + -18t + 3t2 = 0 + -3t2 + 3t2 -12 + -18t + 3t2 = -3t2 + 3t2 Combine like terms: -3t2 + 3t2 = 0 -12 + -18t + 3t2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-4 + -6t + t2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-4 + -6t + t2)' equal to zero and attempt to solve: Simplifying -4 + -6t + t2 = 0 Solving -4 + -6t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + -6t + 4 + t2 = 0 + 4 Reorder the terms: -4 + 4 + -6t + t2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -6t + t2 = 0 + 4 -6t + t2 = 0 + 4 Combine like terms: 0 + 4 = 4 -6t + t2 = 4 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 = 4 + 9 Reorder the terms: 9 + -6t + t2 = 4 + 9 Combine like terms: 4 + 9 = 13 9 + -6t + t2 = 13 Factor a perfect square on the left side: (t + -3)(t + -3) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (t + -3) equal to 3.605551275 and -3.605551275.Subproblem 1
t + -3 = 3.605551275 Simplifying t + -3 = 3.605551275 Reorder the terms: -3 + t = 3.605551275 Solving -3 + t = 3.605551275 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 = 3.605551275 + 3 Combine like terms: -3 + 3 = 0 0 + t = 3.605551275 + 3 t = 3.605551275 + 3 Combine like terms: 3.605551275 + 3 = 6.605551275 t = 6.605551275 Simplifying t = 6.605551275Subproblem 2
t + -3 = -3.605551275 Simplifying t + -3 = -3.605551275 Reorder the terms: -3 + t = -3.605551275 Solving -3 + t = -3.605551275 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 = -3.605551275 + 3 Combine like terms: -3 + 3 = 0 0 + t = -3.605551275 + 3 t = -3.605551275 + 3 Combine like terms: -3.605551275 + 3 = -0.605551275 t = -0.605551275 Simplifying t = -0.605551275Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.605551275, -0.605551275}Solution
t = {6.605551275, -0.605551275}
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