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Simplifying 12x2 + 60x + 147 = 0 Reorder the terms: 147 + 60x + 12x2 = 0 Solving 147 + 60x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(49 + 20x + 4x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(49 + 20x + 4x2)' equal to zero and attempt to solve: Simplifying 49 + 20x + 4x2 = 0 Solving 49 + 20x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 12.25 + 5x + x2 = 0 Move the constant term to the right: Add '-12.25' to each side of the equation. 12.25 + 5x + -12.25 + x2 = 0 + -12.25 Reorder the terms: 12.25 + -12.25 + 5x + x2 = 0 + -12.25 Combine like terms: 12.25 + -12.25 = 0.00 0.00 + 5x + x2 = 0 + -12.25 5x + x2 = 0 + -12.25 Combine like terms: 0 + -12.25 = -12.25 5x + x2 = -12.25 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = -12.25 + 6.25 Reorder the terms: 6.25 + 5x + x2 = -12.25 + 6.25 Combine like terms: -12.25 + 6.25 = -6 6.25 + 5x + x2 = -6 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = -6 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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