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Simplifying -6g2 + -6g + 1 = 0 Reorder the terms: 1 + -6g + -6g2 = 0 Solving 1 + -6g + -6g2 = 0 Solving for variable 'g'. Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -0.1666666667 + g + g2 = 0 Move the constant term to the right: Add '0.1666666667' to each side of the equation. -0.1666666667 + g + 0.1666666667 + g2 = 0 + 0.1666666667 Reorder the terms: -0.1666666667 + 0.1666666667 + g + g2 = 0 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + g + g2 = 0 + 0.1666666667 g + g2 = 0 + 0.1666666667 Combine like terms: 0 + 0.1666666667 = 0.1666666667 g + g2 = 0.1666666667 The g term is g. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + g2 = 0.1666666667 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + g2 = 0.1666666667 + 0.25 Combine like terms: 0.1666666667 + 0.25 = 0.4166666667 1.25 + g2 = 0.4166666667 Factor a perfect square on the left side: (g + 0.5)(g + 0.5) = 0.4166666667 Calculate the square root of the right side: 0.645497224 Break this problem into two subproblems by setting (g + 0.5) equal to 0.645497224 and -0.645497224.Subproblem 1
g + 0.5 = 0.645497224 Simplifying g + 0.5 = 0.645497224 Reorder the terms: 0.5 + g = 0.645497224 Solving 0.5 + g = 0.645497224 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + g = 0.645497224 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + g = 0.645497224 + -0.5 g = 0.645497224 + -0.5 Combine like terms: 0.645497224 + -0.5 = 0.145497224 g = 0.145497224 Simplifying g = 0.145497224Subproblem 2
g + 0.5 = -0.645497224 Simplifying g + 0.5 = -0.645497224 Reorder the terms: 0.5 + g = -0.645497224 Solving 0.5 + g = -0.645497224 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + g = -0.645497224 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + g = -0.645497224 + -0.5 g = -0.645497224 + -0.5 Combine like terms: -0.645497224 + -0.5 = -1.145497224 g = -1.145497224 Simplifying g = -1.145497224Solution
The solution to the problem is based on the solutions from the subproblems. g = {0.145497224, -1.145497224}
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