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Simplifying 24x2 + 24x + 22 = 0 Reorder the terms: 22 + 24x + 24x2 = 0 Solving 22 + 24x + 24x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(11 + 12x + 12x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(11 + 12x + 12x2)' equal to zero and attempt to solve: Simplifying 11 + 12x + 12x2 = 0 Solving 11 + 12x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 0.9166666667 + x + x2 = 0 Move the constant term to the right: Add '-0.9166666667' to each side of the equation. 0.9166666667 + x + -0.9166666667 + x2 = 0 + -0.9166666667 Reorder the terms: 0.9166666667 + -0.9166666667 + x + x2 = 0 + -0.9166666667 Combine like terms: 0.9166666667 + -0.9166666667 = 0.0000000000 0.0000000000 + x + x2 = 0 + -0.9166666667 x + x2 = 0 + -0.9166666667 Combine like terms: 0 + -0.9166666667 = -0.9166666667 x + x2 = -0.9166666667 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 = -0.9166666667 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = -0.9166666667 + 0.25 Combine like terms: -0.9166666667 + 0.25 = -0.6666666667 1.25 + x2 = -0.6666666667 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -0.6666666667 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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