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Simplifying 12x2 + 55x + 63 = x Reorder the terms: 63 + 55x + 12x2 = x Solving 63 + 55x + 12x2 = x Solving for variable 'x'. Reorder the terms: 63 + 55x + -1x + 12x2 = x + -1x Combine like terms: 55x + -1x = 54x 63 + 54x + 12x2 = x + -1x Combine like terms: x + -1x = 0 63 + 54x + 12x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(21 + 18x + 4x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(21 + 18x + 4x2)' equal to zero and attempt to solve: Simplifying 21 + 18x + 4x2 = 0 Solving 21 + 18x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 5.25 + 4.5x + x2 = 0 Move the constant term to the right: Add '-5.25' to each side of the equation. 5.25 + 4.5x + -5.25 + x2 = 0 + -5.25 Reorder the terms: 5.25 + -5.25 + 4.5x + x2 = 0 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + 4.5x + x2 = 0 + -5.25 4.5x + x2 = 0 + -5.25 Combine like terms: 0 + -5.25 = -5.25 4.5x + x2 = -5.25 The x term is 4.5x. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5x + 5.0625 + x2 = -5.25 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = -5.25 + 5.0625 Combine like terms: -5.25 + 5.0625 = -0.1875 5.0625 + 4.5x + x2 = -0.1875 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = -0.1875 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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