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Simplifying 24x2 + 16x + 12 = 0 Reorder the terms: 12 + 16x + 24x2 = 0 Solving 12 + 16x + 24x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(3 + 4x + 6x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(3 + 4x + 6x2)' equal to zero and attempt to solve: Simplifying 3 + 4x + 6x2 = 0 Solving 3 + 4x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.5 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + 0.6666666667x + -0.5 + x2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + 0.6666666667x + x2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + 0.6666666667x + x2 = 0 + -0.5 0.6666666667x + x2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 0.6666666667x + x2 = -0.5 The x term is 0.6666666667x. Take half its coefficient (0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. 0.6666666667x + 0.1111111112 + x2 = -0.5 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = -0.5 + 0.1111111112 Combine like terms: -0.5 + 0.1111111112 = -0.3888888888 0.1111111112 + 0.6666666667x + x2 = -0.3888888888 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = -0.3888888888 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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