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Simplifying 24x2 + 16x + 144 = 0 Reorder the terms: 144 + 16x + 24x2 = 0 Solving 144 + 16x + 24x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '8'. 8(18 + 2x + 3x2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(18 + 2x + 3x2)' equal to zero and attempt to solve: Simplifying 18 + 2x + 3x2 = 0 Solving 18 + 2x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 6 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '-6' to each side of the equation. 6 + 0.6666666667x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + 0.6666666667x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 0.6666666667x + x2 = 0 + -6 0.6666666667x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 0.6666666667x + x2 = -6 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 = -6 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = -6 + 0.1111111112 Combine like terms: -6 + 0.1111111112 = -5.8888888888 0.1111111112 + 0.6666666667x + x2 = -5.8888888888 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = -5.8888888888 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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