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Simplifying 24x2 + 24x + 9 = 0 Reorder the terms: 9 + 24x + 24x2 = 0 Solving 9 + 24x + 24x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(3 + 8x + 8x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(3 + 8x + 8x2)' equal to zero and attempt to solve: Simplifying 3 + 8x + 8x2 = 0 Solving 3 + 8x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.375 + x + x2 = 0 Move the constant term to the right: Add '-0.375' to each side of the equation. 0.375 + x + -0.375 + x2 = 0 + -0.375 Reorder the terms: 0.375 + -0.375 + x + x2 = 0 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x + x2 = 0 + -0.375 x + x2 = 0 + -0.375 Combine like terms: 0 + -0.375 = -0.375 x + x2 = -0.375 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. + 0.25 + x2 = -0.375 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = -0.375 + 0.25 Combine like terms: -0.375 + 0.25 = -0.125 1.25 + x2 = -0.125 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -0.125 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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