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Simplifying 5g2 + 8g + -6 = 0 Reorder the terms: -6 + 8g + 5g2 = 0 Solving -6 + 8g + 5g2 = 0 Solving for variable 'g'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.2 + 1.6g + g2 = 0 Move the constant term to the right: Add '1.2' to each side of the equation. -1.2 + 1.6g + 1.2 + g2 = 0 + 1.2 Reorder the terms: -1.2 + 1.2 + 1.6g + g2 = 0 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + 1.6g + g2 = 0 + 1.2 1.6g + g2 = 0 + 1.2 Combine like terms: 0 + 1.2 = 1.2 1.6g + g2 = 1.2 The g term is 1.6g. Take half its coefficient (0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. 1.6g + 0.64 + g2 = 1.2 + 0.64 Reorder the terms: 0.64 + 1.6g + g2 = 1.2 + 0.64 Combine like terms: 1.2 + 0.64 = 1.84 0.64 + 1.6g + g2 = 1.84 Factor a perfect square on the left side: (g + 0.8)(g + 0.8) = 1.84 Calculate the square root of the right side: 1.356465997 Break this problem into two subproblems by setting (g + 0.8) equal to 1.356465997 and -1.356465997.Subproblem 1
g + 0.8 = 1.356465997 Simplifying g + 0.8 = 1.356465997 Reorder the terms: 0.8 + g = 1.356465997 Solving 0.8 + g = 1.356465997 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + g = 1.356465997 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + g = 1.356465997 + -0.8 g = 1.356465997 + -0.8 Combine like terms: 1.356465997 + -0.8 = 0.556465997 g = 0.556465997 Simplifying g = 0.556465997Subproblem 2
g + 0.8 = -1.356465997 Simplifying g + 0.8 = -1.356465997 Reorder the terms: 0.8 + g = -1.356465997 Solving 0.8 + g = -1.356465997 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + g = -1.356465997 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + g = -1.356465997 + -0.8 g = -1.356465997 + -0.8 Combine like terms: -1.356465997 + -0.8 = -2.156465997 g = -2.156465997 Simplifying g = -2.156465997Solution
The solution to the problem is based on the solutions from the subproblems. g = {0.556465997, -2.156465997}
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