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Simplifying 3t2 + 6t = 18 Reorder the terms: 6t + 3t2 = 18 Solving 6t + 3t2 = 18 Solving for variable 't'. Reorder the terms: -18 + 6t + 3t2 = 18 + -18 Combine like terms: 18 + -18 = 0 -18 + 6t + 3t2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-6 + 2t + t2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-6 + 2t + t2)' equal to zero and attempt to solve: Simplifying -6 + 2t + t2 = 0 Solving -6 + 2t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + 2t + 6 + t2 = 0 + 6 Reorder the terms: -6 + 6 + 2t + t2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 2t + t2 = 0 + 6 2t + t2 = 0 + 6 Combine like terms: 0 + 6 = 6 2t + t2 = 6 The t term is 2t. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2t + 1 + t2 = 6 + 1 Reorder the terms: 1 + 2t + t2 = 6 + 1 Combine like terms: 6 + 1 = 7 1 + 2t + t2 = 7 Factor a perfect square on the left side: (t + 1)(t + 1) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (t + 1) equal to 2.645751311 and -2.645751311.Subproblem 1
t + 1 = 2.645751311 Simplifying t + 1 = 2.645751311 Reorder the terms: 1 + t = 2.645751311 Solving 1 + t = 2.645751311 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + t = 2.645751311 + -1 Combine like terms: 1 + -1 = 0 0 + t = 2.645751311 + -1 t = 2.645751311 + -1 Combine like terms: 2.645751311 + -1 = 1.645751311 t = 1.645751311 Simplifying t = 1.645751311Subproblem 2
t + 1 = -2.645751311 Simplifying t + 1 = -2.645751311 Reorder the terms: 1 + t = -2.645751311 Solving 1 + t = -2.645751311 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + t = -2.645751311 + -1 Combine like terms: 1 + -1 = 0 0 + t = -2.645751311 + -1 t = -2.645751311 + -1 Combine like terms: -2.645751311 + -1 = -3.645751311 t = -3.645751311 Simplifying t = -3.645751311Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.645751311, -3.645751311}Solution
t = {1.645751311, -3.645751311}
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