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Simplifying r2 + 10rg + 10g2 = 0 Reorder the terms: 10gr + 10g2 + r2 = 0 Solving 10gr + 10g2 + r2 = 0 Solving for variable 'g'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. gr + g2 + 0.1r2 = 0 Move the constant term to the right: Add '-1r2' to each side of the equation. gr + g2 + 0.1r2 + -1r2 = 0 + -1r2 Combine like terms: 0.1r2 + -1r2 = -0.9r2 gr + g2 + -0.9r2 = 0 + -1r2 Remove the zero: gr + g2 + -0.9r2 = -1r2 The g term is gr. Take half its coefficient (0.5r). Square it (0.25r2) and add it to both sides. Add '0.25r2' to each side of the equation. r2 + g2 + -0.9r2 + 0.25r2 = -1r2 + 0.25r2 Reorder the terms: g2 + r2 + -0.9r2 + 0.25r2 = -1r2 + 0.25r2 Combine like terms: r2 + -0.9r2 = 0.1r2 g2 + 0.1r2 + 0.25r2 = -1r2 + 0.25r2 Combine like terms: 0.1r2 + 0.25r2 = 0.35r2 g2 + 0.35r2 = -1r2 + 0.25r2 Combine like terms: -1r2 + 0.25r2 = -0.75r2 g2 + 0.35r2 = -0.75r2 Factor a perfect square on the left side: (g + 0.5r)(g + 0.5r) = -0.75r2 Can't calculate square root of the right side. The solution to this equation could not be determined.
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