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Simplifying 6x2 + 27x + 18 = 0 Reorder the terms: 18 + 27x + 6x2 = 0 Solving 18 + 27x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(6 + 9x + 2x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(6 + 9x + 2x2)' equal to zero and attempt to solve: Simplifying 6 + 9x + 2x2 = 0 Solving 6 + 9x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 3 + 4.5x + x2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + 4.5x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + 4.5x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4.5x + x2 = 0 + -3 4.5x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 4.5x + x2 = -3 The x term is 4.5x. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5x + 5.0625 + x2 = -3 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = -3 + 5.0625 Combine like terms: -3 + 5.0625 = 2.0625 5.0625 + 4.5x + x2 = 2.0625 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 2.0625 Calculate the square root of the right side: 1.436140662 Break this problem into two subproblems by setting (x + 2.25) equal to 1.436140662 and -1.436140662.Subproblem 1
x + 2.25 = 1.436140662 Simplifying x + 2.25 = 1.436140662 Reorder the terms: 2.25 + x = 1.436140662 Solving 2.25 + x = 1.436140662 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = 1.436140662 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 1.436140662 + -2.25 x = 1.436140662 + -2.25 Combine like terms: 1.436140662 + -2.25 = -0.813859338 x = -0.813859338 Simplifying x = -0.813859338Subproblem 2
x + 2.25 = -1.436140662 Simplifying x + 2.25 = -1.436140662 Reorder the terms: 2.25 + x = -1.436140662 Solving 2.25 + x = -1.436140662 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = -1.436140662 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -1.436140662 + -2.25 x = -1.436140662 + -2.25 Combine like terms: -1.436140662 + -2.25 = -3.686140662 x = -3.686140662 Simplifying x = -3.686140662Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.813859338, -3.686140662}Solution
x = {-0.813859338, -3.686140662}
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