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Simplifying 9(x2 + 6x + 6) = 0 Reorder the terms: 9(6 + 6x + x2) = 0 (6 * 9 + 6x * 9 + x2 * 9) = 0 (54 + 54x + 9x2) = 0 Solving 54 + 54x + 9x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '9'. 9(6 + 6x + x2) = 0 Ignore the factor 9.Subproblem 1
Set the factor '(6 + 6x + x2)' equal to zero and attempt to solve: Simplifying 6 + 6x + x2 = 0 Solving 6 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + 6x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + 6x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 6x + x2 = 0 + -6 6x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 6x + x2 = -6 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = -6 + 9 Reorder the terms: 9 + 6x + x2 = -6 + 9 Combine like terms: -6 + 9 = 3 9 + 6x + x2 = 3 Factor a perfect square on the left side: (x + 3)(x + 3) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (x + 3) equal to 1.732050808 and -1.732050808.Subproblem 1
x + 3 = 1.732050808 Simplifying x + 3 = 1.732050808 Reorder the terms: 3 + x = 1.732050808 Solving 3 + x = 1.732050808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 1.732050808 + -3 Combine like terms: 3 + -3 = 0 0 + x = 1.732050808 + -3 x = 1.732050808 + -3 Combine like terms: 1.732050808 + -3 = -1.267949192 x = -1.267949192 Simplifying x = -1.267949192Subproblem 2
x + 3 = -1.732050808 Simplifying x + 3 = -1.732050808 Reorder the terms: 3 + x = -1.732050808 Solving 3 + x = -1.732050808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -1.732050808 + -3 Combine like terms: 3 + -3 = 0 0 + x = -1.732050808 + -3 x = -1.732050808 + -3 Combine like terms: -1.732050808 + -3 = -4.732050808 x = -4.732050808 Simplifying x = -4.732050808Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.267949192, -4.732050808}Solution
x = {-1.267949192, -4.732050808}
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