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Simplifying 9x2 + 54x + -6 = 0 Reorder the terms: -6 + 54x + 9x2 = 0 Solving -6 + 54x + 9x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-2 + 18x + 3x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-2 + 18x + 3x2)' equal to zero and attempt to solve: Simplifying -2 + 18x + 3x2 = 0 Solving -2 + 18x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -0.6666666667 + 6x + x2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + 6x + 0.6666666667 + x2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + 6x + x2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + 6x + x2 = 0 + 0.6666666667 6x + x2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 6x + x2 = 0.6666666667 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 = 0.6666666667 + 9 Reorder the terms: 9 + 6x + x2 = 0.6666666667 + 9 Combine like terms: 0.6666666667 + 9 = 9.6666666667 9 + 6x + x2 = 9.6666666667 Factor a perfect square on the left side: (x + 3)(x + 3) = 9.6666666667 Calculate the square root of the right side: 3.109126351 Break this problem into two subproblems by setting (x + 3) equal to 3.109126351 and -3.109126351.Subproblem 1
x + 3 = 3.109126351 Simplifying x + 3 = 3.109126351 Reorder the terms: 3 + x = 3.109126351 Solving 3 + x = 3.109126351 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 = 3.109126351 + -3 Combine like terms: 3 + -3 = 0 0 + x = 3.109126351 + -3 x = 3.109126351 + -3 Combine like terms: 3.109126351 + -3 = 0.109126351 x = 0.109126351 Simplifying x = 0.109126351Subproblem 2
x + 3 = -3.109126351 Simplifying x + 3 = -3.109126351 Reorder the terms: 3 + x = -3.109126351 Solving 3 + x = -3.109126351 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 = -3.109126351 + -3 Combine like terms: 3 + -3 = 0 0 + x = -3.109126351 + -3 x = -3.109126351 + -3 Combine like terms: -3.109126351 + -3 = -6.109126351 x = -6.109126351 Simplifying x = -6.109126351Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.109126351, -6.109126351}Solution
x = {0.109126351, -6.109126351}
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