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Simplifying 12x2 + 174x + 756 = 0 Reorder the terms: 756 + 174x + 12x2 = 0 Solving 756 + 174x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(126 + 29x + 2x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(126 + 29x + 2x2)' equal to zero and attempt to solve: Simplifying 126 + 29x + 2x2 = 0 Solving 126 + 29x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 63 + 14.5x + x2 = 0 Move the constant term to the right: Add '-63' to each side of the equation. 63 + 14.5x + -63 + x2 = 0 + -63 Reorder the terms: 63 + -63 + 14.5x + x2 = 0 + -63 Combine like terms: 63 + -63 = 0 0 + 14.5x + x2 = 0 + -63 14.5x + x2 = 0 + -63 Combine like terms: 0 + -63 = -63 14.5x + x2 = -63 The x term is 14.5x. Take half its coefficient (7.25). Square it (52.5625) and add it to both sides. Add '52.5625' to each side of the equation. 14.5x + 52.5625 + x2 = -63 + 52.5625 Reorder the terms: 52.5625 + 14.5x + x2 = -63 + 52.5625 Combine like terms: -63 + 52.5625 = -10.4375 52.5625 + 14.5x + x2 = -10.4375 Factor a perfect square on the left side: (x + 7.25)(x + 7.25) = -10.4375 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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