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Simplifying 9x2 + -12x + -108 = 0 Reorder the terms: -108 + -12x + 9x2 = 0 Solving -108 + -12x + 9x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-36 + -4x + 3x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-36 + -4x + 3x2)' equal to zero and attempt to solve: Simplifying -36 + -4x + 3x2 = 0 Solving -36 + -4x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -12 + -1.333333333x + x2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + -1.333333333x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + -1.333333333x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -1.333333333x + x2 = 0 + 12 -1.333333333x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 -1.333333333x + x2 = 12 The x term is -1.333333333x. Take half its coefficient (-0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. -1.333333333x + 0.4444444442 + x2 = 12 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333x + x2 = 12 + 0.4444444442 Combine like terms: 12 + 0.4444444442 = 12.4444444442 0.4444444442 + -1.333333333x + x2 = 12.4444444442 Factor a perfect square on the left side: (x + -0.6666666665)(x + -0.6666666665) = 12.4444444442 Calculate the square root of the right side: 3.527668415 Break this problem into two subproblems by setting (x + -0.6666666665) equal to 3.527668415 and -3.527668415.Subproblem 1
x + -0.6666666665 = 3.527668415 Simplifying x + -0.6666666665 = 3.527668415 Reorder the terms: -0.6666666665 + x = 3.527668415 Solving -0.6666666665 + x = 3.527668415 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + x = 3.527668415 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = 3.527668415 + 0.6666666665 x = 3.527668415 + 0.6666666665 Combine like terms: 3.527668415 + 0.6666666665 = 4.1943350815 x = 4.1943350815 Simplifying x = 4.1943350815Subproblem 2
x + -0.6666666665 = -3.527668415 Simplifying x + -0.6666666665 = -3.527668415 Reorder the terms: -0.6666666665 + x = -3.527668415 Solving -0.6666666665 + x = -3.527668415 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + x = -3.527668415 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = -3.527668415 + 0.6666666665 x = -3.527668415 + 0.6666666665 Combine like terms: -3.527668415 + 0.6666666665 = -2.8610017485 x = -2.8610017485 Simplifying x = -2.8610017485Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.1943350815, -2.8610017485}Solution
x = {4.1943350815, -2.8610017485}
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