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Simplifying 27x2 + 324x = -72 Reorder the terms: 324x + 27x2 = -72 Solving 324x + 27x2 = -72 Solving for variable 'x'. Reorder the terms: 72 + 324x + 27x2 = -72 + 72 Combine like terms: -72 + 72 = 0 72 + 324x + 27x2 = 0 Factor out the Greatest Common Factor (GCF), '9'. 9(8 + 36x + 3x2) = 0 Ignore the factor 9.Subproblem 1
Set the factor '(8 + 36x + 3x2)' equal to zero and attempt to solve: Simplifying 8 + 36x + 3x2 = 0 Solving 8 + 36x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 2.666666667 + 12x + x2 = 0 Move the constant term to the right: Add '-2.666666667' to each side of the equation. 2.666666667 + 12x + -2.666666667 + x2 = 0 + -2.666666667 Reorder the terms: 2.666666667 + -2.666666667 + 12x + x2 = 0 + -2.666666667 Combine like terms: 2.666666667 + -2.666666667 = 0.000000000 0.000000000 + 12x + x2 = 0 + -2.666666667 12x + x2 = 0 + -2.666666667 Combine like terms: 0 + -2.666666667 = -2.666666667 12x + x2 = -2.666666667 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 = -2.666666667 + 36 Reorder the terms: 36 + 12x + x2 = -2.666666667 + 36 Combine like terms: -2.666666667 + 36 = 33.333333333 36 + 12x + x2 = 33.333333333 Factor a perfect square on the left side: (x + 6)(x + 6) = 33.333333333 Calculate the square root of the right side: 5.773502692 Break this problem into two subproblems by setting (x + 6) equal to 5.773502692 and -5.773502692.Subproblem 1
x + 6 = 5.773502692 Simplifying x + 6 = 5.773502692 Reorder the terms: 6 + x = 5.773502692 Solving 6 + x = 5.773502692 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 = 5.773502692 + -6 Combine like terms: 6 + -6 = 0 0 + x = 5.773502692 + -6 x = 5.773502692 + -6 Combine like terms: 5.773502692 + -6 = -0.226497308 x = -0.226497308 Simplifying x = -0.226497308Subproblem 2
x + 6 = -5.773502692 Simplifying x + 6 = -5.773502692 Reorder the terms: 6 + x = -5.773502692 Solving 6 + x = -5.773502692 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 = -5.773502692 + -6 Combine like terms: 6 + -6 = 0 0 + x = -5.773502692 + -6 x = -5.773502692 + -6 Combine like terms: -5.773502692 + -6 = -11.773502692 x = -11.773502692 Simplifying x = -11.773502692Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.226497308, -11.773502692}Solution
x = {-0.226497308, -11.773502692}
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