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Simplifying 7t2 + 42t + -126 = 0 Reorder the terms: -126 + 42t + 7t2 = 0 Solving -126 + 42t + 7t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '7'. 7(-18 + 6t + t2) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(-18 + 6t + t2)' equal to zero and attempt to solve: Simplifying -18 + 6t + t2 = 0 Solving -18 + 6t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + 6t + 18 + t2 = 0 + 18 Reorder the terms: -18 + 18 + 6t + t2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + 6t + t2 = 0 + 18 6t + t2 = 0 + 18 Combine like terms: 0 + 18 = 18 6t + t2 = 18 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 = 18 + 9 Reorder the terms: 9 + 6t + t2 = 18 + 9 Combine like terms: 18 + 9 = 27 9 + 6t + t2 = 27 Factor a perfect square on the left side: (t + 3)(t + 3) = 27 Calculate the square root of the right side: 5.196152423 Break this problem into two subproblems by setting (t + 3) equal to 5.196152423 and -5.196152423.Subproblem 1
t + 3 = 5.196152423 Simplifying t + 3 = 5.196152423 Reorder the terms: 3 + t = 5.196152423 Solving 3 + t = 5.196152423 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 = 5.196152423 + -3 Combine like terms: 3 + -3 = 0 0 + t = 5.196152423 + -3 t = 5.196152423 + -3 Combine like terms: 5.196152423 + -3 = 2.196152423 t = 2.196152423 Simplifying t = 2.196152423Subproblem 2
t + 3 = -5.196152423 Simplifying t + 3 = -5.196152423 Reorder the terms: 3 + t = -5.196152423 Solving 3 + t = -5.196152423 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 = -5.196152423 + -3 Combine like terms: 3 + -3 = 0 0 + t = -5.196152423 + -3 t = -5.196152423 + -3 Combine like terms: -5.196152423 + -3 = -8.196152423 t = -8.196152423 Simplifying t = -8.196152423Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.196152423, -8.196152423}Solution
t = {2.196152423, -8.196152423}
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