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Simplifying 3x2 + 24x2 + 3x + 24 = 0 Reorder the terms: 24 + 3x + 3x2 + 24x2 = 0 Combine like terms: 3x2 + 24x2 = 27x2 24 + 3x + 27x2 = 0 Solving 24 + 3x + 27x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(8 + x + 9x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(8 + x + 9x2)' equal to zero and attempt to solve: Simplifying 8 + x + 9x2 = 0 Solving 8 + x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.8888888889 + 0.1111111111x + x2 = 0 Move the constant term to the right: Add '-0.8888888889' to each side of the equation. 0.8888888889 + 0.1111111111x + -0.8888888889 + x2 = 0 + -0.8888888889 Reorder the terms: 0.8888888889 + -0.8888888889 + 0.1111111111x + x2 = 0 + -0.8888888889 Combine like terms: 0.8888888889 + -0.8888888889 = 0.0000000000 0.0000000000 + 0.1111111111x + x2 = 0 + -0.8888888889 0.1111111111x + x2 = 0 + -0.8888888889 Combine like terms: 0 + -0.8888888889 = -0.8888888889 0.1111111111x + x2 = -0.8888888889 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.1111111111x + 0.25 + x2 = -0.8888888889 + 0.25 Reorder the terms: 0.25 + 0.1111111111x + x2 = -0.8888888889 + 0.25 Combine like terms: -0.8888888889 + 0.25 = -0.6388888889 0.25 + 0.1111111111x + x2 = -0.6388888889 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -0.6388888889 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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