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Simplifying -6g2 + -8g + 6 = 0 Reorder the terms: 6 + -8g + -6g2 = 0 Solving 6 + -8g + -6g2 = 0 Solving for variable 'g'. Factor out the Greatest Common Factor (GCF), '2'. 2(3 + -4g + -3g2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + -4g + -3g2)' equal to zero and attempt to solve: Simplifying 3 + -4g + -3g2 = 0 Solving 3 + -4g + -3g2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -1 + 1.333333333g + g2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 1.333333333g + 1 + g2 = 0 + 1 Reorder the terms: -1 + 1 + 1.333333333g + g2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 1.333333333g + g2 = 0 + 1 1.333333333g + g2 = 0 + 1 Combine like terms: 0 + 1 = 1 1.333333333g + g2 = 1 The g term is 1.333333333g. Take half its coefficient (0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. 1.333333333g + 0.4444444442 + g2 = 1 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333g + g2 = 1 + 0.4444444442 Combine like terms: 1 + 0.4444444442 = 1.4444444442 0.4444444442 + 1.333333333g + g2 = 1.4444444442 Factor a perfect square on the left side: (g + 0.6666666665)(g + 0.6666666665) = 1.4444444442 Calculate the square root of the right side: 1.201850425 Break this problem into two subproblems by setting (g + 0.6666666665) equal to 1.201850425 and -1.201850425.Subproblem 1
g + 0.6666666665 = 1.201850425 Simplifying g + 0.6666666665 = 1.201850425 Reorder the terms: 0.6666666665 + g = 1.201850425 Solving 0.6666666665 + g = 1.201850425 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + g = 1.201850425 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + g = 1.201850425 + -0.6666666665 g = 1.201850425 + -0.6666666665 Combine like terms: 1.201850425 + -0.6666666665 = 0.5351837585 g = 0.5351837585 Simplifying g = 0.5351837585Subproblem 2
g + 0.6666666665 = -1.201850425 Simplifying g + 0.6666666665 = -1.201850425 Reorder the terms: 0.6666666665 + g = -1.201850425 Solving 0.6666666665 + g = -1.201850425 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + g = -1.201850425 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + g = -1.201850425 + -0.6666666665 g = -1.201850425 + -0.6666666665 Combine like terms: -1.201850425 + -0.6666666665 = -1.8685170915 g = -1.8685170915 Simplifying g = -1.8685170915Solution
The solution to the problem is based on the solutions from the subproblems. g = {0.5351837585, -1.8685170915}Solution
g = {0.5351837585, -1.8685170915}
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