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Simplifying 4x2 + 78x + 672 = 0 Reorder the terms: 672 + 78x + 4x2 = 0 Solving 672 + 78x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(336 + 39x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(336 + 39x + 2x2)' equal to zero and attempt to solve: Simplifying 336 + 39x + 2x2 = 0 Solving 336 + 39x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 168 + 19.5x + x2 = 0 Move the constant term to the right: Add '-168' to each side of the equation. 168 + 19.5x + -168 + x2 = 0 + -168 Reorder the terms: 168 + -168 + 19.5x + x2 = 0 + -168 Combine like terms: 168 + -168 = 0 0 + 19.5x + x2 = 0 + -168 19.5x + x2 = 0 + -168 Combine like terms: 0 + -168 = -168 19.5x + x2 = -168 The x term is 19.5x. Take half its coefficient (9.75). Square it (95.0625) and add it to both sides. Add '95.0625' to each side of the equation. 19.5x + 95.0625 + x2 = -168 + 95.0625 Reorder the terms: 95.0625 + 19.5x + x2 = -168 + 95.0625 Combine like terms: -168 + 95.0625 = -72.9375 95.0625 + 19.5x + x2 = -72.9375 Factor a perfect square on the left side: (x + 9.75)(x + 9.75) = -72.9375 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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