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Simplifying g2 + 20g + 11 = -69 Reorder the terms: 11 + 20g + g2 = -69 Solving 11 + 20g + g2 = -69 Solving for variable 'g'. Reorder the terms: 11 + 69 + 20g + g2 = -69 + 69 Combine like terms: 11 + 69 = 80 80 + 20g + g2 = -69 + 69 Combine like terms: -69 + 69 = 0 80 + 20g + g2 = 0 Begin completing the square. Move the constant term to the right: Add '-80' to each side of the equation. 80 + 20g + -80 + g2 = 0 + -80 Reorder the terms: 80 + -80 + 20g + g2 = 0 + -80 Combine like terms: 80 + -80 = 0 0 + 20g + g2 = 0 + -80 20g + g2 = 0 + -80 Combine like terms: 0 + -80 = -80 20g + g2 = -80 The g term is 20g. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20g + 100 + g2 = -80 + 100 Reorder the terms: 100 + 20g + g2 = -80 + 100 Combine like terms: -80 + 100 = 20 100 + 20g + g2 = 20 Factor a perfect square on the left side: (g + 10)(g + 10) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (g + 10) equal to 4.472135955 and -4.472135955.Subproblem 1
g + 10 = 4.472135955 Simplifying g + 10 = 4.472135955 Reorder the terms: 10 + g = 4.472135955 Solving 10 + g = 4.472135955 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + g = 4.472135955 + -10 Combine like terms: 10 + -10 = 0 0 + g = 4.472135955 + -10 g = 4.472135955 + -10 Combine like terms: 4.472135955 + -10 = -5.527864045 g = -5.527864045 Simplifying g = -5.527864045Subproblem 2
g + 10 = -4.472135955 Simplifying g + 10 = -4.472135955 Reorder the terms: 10 + g = -4.472135955 Solving 10 + g = -4.472135955 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + g = -4.472135955 + -10 Combine like terms: 10 + -10 = 0 0 + g = -4.472135955 + -10 g = -4.472135955 + -10 Combine like terms: -4.472135955 + -10 = -14.472135955 g = -14.472135955 Simplifying g = -14.472135955Solution
The solution to the problem is based on the solutions from the subproblems. g = {-5.527864045, -14.472135955}
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