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Simplifying r2 + -2rg + -63g2 = 0 Reorder the terms: -2gr + -63g2 + r2 = 0 Solving -2gr + -63g2 + r2 = 0 Solving for variable 'g'. Factor a trinomial. (-7g + -1r)(9g + -1r) = 0Subproblem 1
Set the factor '(-7g + -1r)' equal to zero and attempt to solve: Simplifying -7g + -1r = 0 Solving -7g + -1r = 0 Move all terms containing g to the left, all other terms to the right. Add 'r' to each side of the equation. -7g + -1r + r = 0 + r Combine like terms: -1r + r = 0 -7g + 0 = 0 + r -7g = 0 + r Remove the zero: -7g = r Divide each side by '-7'. g = -0.1428571429r Simplifying g = -0.1428571429rSubproblem 2
Set the factor '(9g + -1r)' equal to zero and attempt to solve: Simplifying 9g + -1r = 0 Solving 9g + -1r = 0 Move all terms containing g to the left, all other terms to the right. Add 'r' to each side of the equation. 9g + -1r + r = 0 + r Combine like terms: -1r + r = 0 9g + 0 = 0 + r 9g = 0 + r Remove the zero: 9g = r Divide each side by '9'. g = 0.1111111111r Simplifying g = 0.1111111111rSolution
g = {-0.1428571429r, 0.1111111111r}
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