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Simplifying 8x2 + 18x + 24 = 0 Reorder the terms: 24 + 18x + 8x2 = 0 Solving 24 + 18x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(12 + 9x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(12 + 9x + 4x2)' equal to zero and attempt to solve: Simplifying 12 + 9x + 4x2 = 0 Solving 12 + 9x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 3 + 2.25x + x2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + 2.25x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + 2.25x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2.25x + x2 = 0 + -3 2.25x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 2.25x + x2 = -3 The x term is 2.25x. Take half its coefficient (1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. 2.25x + 1.265625 + x2 = -3 + 1.265625 Reorder the terms: 1.265625 + 2.25x + x2 = -3 + 1.265625 Combine like terms: -3 + 1.265625 = -1.734375 1.265625 + 2.25x + x2 = -1.734375 Factor a perfect square on the left side: (x + 1.125)(x + 1.125) = -1.734375 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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