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Simplifying 3x2 + 36x + 27 = 0 Reorder the terms: 27 + 36x + 3x2 = 0 Solving 27 + 36x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(9 + 12x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(9 + 12x + x2)' equal to zero and attempt to solve: Simplifying 9 + 12x + x2 = 0 Solving 9 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + 12x + -9 + x2 = 0 + -9 Reorder the terms: 9 + -9 + 12x + x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 12x + x2 = 0 + -9 12x + x2 = 0 + -9 Combine like terms: 0 + -9 = -9 12x + x2 = -9 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = -9 + 36 Reorder the terms: 36 + 12x + x2 = -9 + 36 Combine like terms: -9 + 36 = 27 36 + 12x + x2 = 27 Factor a perfect square on the left side: (x + 6)(x + 6) = 27 Calculate the square root of the right side: 5.196152423 Break this problem into two subproblems by setting (x + 6) equal to 5.196152423 and -5.196152423.Subproblem 1
x + 6 = 5.196152423 Simplifying x + 6 = 5.196152423 Reorder the terms: 6 + x = 5.196152423 Solving 6 + x = 5.196152423 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 5.196152423 + -6 Combine like terms: 6 + -6 = 0 0 + x = 5.196152423 + -6 x = 5.196152423 + -6 Combine like terms: 5.196152423 + -6 = -0.803847577 x = -0.803847577 Simplifying x = -0.803847577Subproblem 2
x + 6 = -5.196152423 Simplifying x + 6 = -5.196152423 Reorder the terms: 6 + x = -5.196152423 Solving 6 + x = -5.196152423 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -5.196152423 + -6 Combine like terms: 6 + -6 = 0 0 + x = -5.196152423 + -6 x = -5.196152423 + -6 Combine like terms: -5.196152423 + -6 = -11.196152423 x = -11.196152423 Simplifying x = -11.196152423Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.803847577, -11.196152423}Solution
x = {-0.803847577, -11.196152423}
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