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Simplifying 4g2 + -2g2 + 2g + -3g + 7 = 0 Reorder the terms: 7 + 2g + -3g + 4g2 + -2g2 = 0 Combine like terms: 2g + -3g = -1g 7 + -1g + 4g2 + -2g2 = 0 Combine like terms: 4g2 + -2g2 = 2g2 7 + -1g + 2g2 = 0 Solving 7 + -1g + 2g2 = 0 Solving for variable 'g'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 3.5 + -0.5g + g2 = 0 Move the constant term to the right: Add '-3.5' to each side of the equation. 3.5 + -0.5g + -3.5 + g2 = 0 + -3.5 Reorder the terms: 3.5 + -3.5 + -0.5g + g2 = 0 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + -0.5g + g2 = 0 + -3.5 -0.5g + g2 = 0 + -3.5 Combine like terms: 0 + -3.5 = -3.5 -0.5g + g2 = -3.5 The g term is -0.5g. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5g + 0.0625 + g2 = -3.5 + 0.0625 Reorder the terms: 0.0625 + -0.5g + g2 = -3.5 + 0.0625 Combine like terms: -3.5 + 0.0625 = -3.4375 0.0625 + -0.5g + g2 = -3.4375 Factor a perfect square on the left side: (g + -0.25)(g + -0.25) = -3.4375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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