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Simplifying 3t2 + -18t = 51 Reorder the terms: -18t + 3t2 = 51 Solving -18t + 3t2 = 51 Solving for variable 't'. Reorder the terms: -51 + -18t + 3t2 = 51 + -51 Combine like terms: 51 + -51 = 0 -51 + -18t + 3t2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-17 + -6t + t2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-17 + -6t + t2)' equal to zero and attempt to solve: Simplifying -17 + -6t + t2 = 0 Solving -17 + -6t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '17' to each side of the equation. -17 + -6t + 17 + t2 = 0 + 17 Reorder the terms: -17 + 17 + -6t + t2 = 0 + 17 Combine like terms: -17 + 17 = 0 0 + -6t + t2 = 0 + 17 -6t + t2 = 0 + 17 Combine like terms: 0 + 17 = 17 -6t + t2 = 17 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 = 17 + 9 Reorder the terms: 9 + -6t + t2 = 17 + 9 Combine like terms: 17 + 9 = 26 9 + -6t + t2 = 26 Factor a perfect square on the left side: (t + -3)(t + -3) = 26 Calculate the square root of the right side: 5.099019514 Break this problem into two subproblems by setting (t + -3) equal to 5.099019514 and -5.099019514.Subproblem 1
t + -3 = 5.099019514 Simplifying t + -3 = 5.099019514 Reorder the terms: -3 + t = 5.099019514 Solving -3 + t = 5.099019514 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 = 5.099019514 + 3 Combine like terms: -3 + 3 = 0 0 + t = 5.099019514 + 3 t = 5.099019514 + 3 Combine like terms: 5.099019514 + 3 = 8.099019514 t = 8.099019514 Simplifying t = 8.099019514Subproblem 2
t + -3 = -5.099019514 Simplifying t + -3 = -5.099019514 Reorder the terms: -3 + t = -5.099019514 Solving -3 + t = -5.099019514 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 = -5.099019514 + 3 Combine like terms: -3 + 3 = 0 0 + t = -5.099019514 + 3 t = -5.099019514 + 3 Combine like terms: -5.099019514 + 3 = -2.099019514 t = -2.099019514 Simplifying t = -2.099019514Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.099019514, -2.099019514}Solution
t = {8.099019514, -2.099019514}
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