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Simplifying 4x2 + 24x + 138 = 0 Reorder the terms: 138 + 24x + 4x2 = 0 Solving 138 + 24x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(69 + 12x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(69 + 12x + 2x2)' equal to zero and attempt to solve: Simplifying 69 + 12x + 2x2 = 0 Solving 69 + 12x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 34.5 + 6x + x2 = 0 Move the constant term to the right: Add '-34.5' to each side of the equation. 34.5 + 6x + -34.5 + x2 = 0 + -34.5 Reorder the terms: 34.5 + -34.5 + 6x + x2 = 0 + -34.5 Combine like terms: 34.5 + -34.5 = 0.0 0.0 + 6x + x2 = 0 + -34.5 6x + x2 = 0 + -34.5 Combine like terms: 0 + -34.5 = -34.5 6x + x2 = -34.5 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = -34.5 + 9 Reorder the terms: 9 + 6x + x2 = -34.5 + 9 Combine like terms: -34.5 + 9 = -25.5 9 + 6x + x2 = -25.5 Factor a perfect square on the left side: (x + 3)(x + 3) = -25.5 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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