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Simplifying g2 + 20g + 94 = 0 Reorder the terms: 94 + 20g + g2 = 0 Solving 94 + 20g + g2 = 0 Solving for variable 'g'. Begin completing the square. Move the constant term to the right: Add '-94' to each side of the equation. 94 + 20g + -94 + g2 = 0 + -94 Reorder the terms: 94 + -94 + 20g + g2 = 0 + -94 Combine like terms: 94 + -94 = 0 0 + 20g + g2 = 0 + -94 20g + g2 = 0 + -94 Combine like terms: 0 + -94 = -94 20g + g2 = -94 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 = -94 + 100 Reorder the terms: 100 + 20g + g2 = -94 + 100 Combine like terms: -94 + 100 = 6 100 + 20g + g2 = 6 Factor a perfect square on the left side: (g + 10)(g + 10) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (g + 10) equal to 2.449489743 and -2.449489743.Subproblem 1
g + 10 = 2.449489743 Simplifying g + 10 = 2.449489743 Reorder the terms: 10 + g = 2.449489743 Solving 10 + g = 2.449489743 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 = 2.449489743 + -10 Combine like terms: 10 + -10 = 0 0 + g = 2.449489743 + -10 g = 2.449489743 + -10 Combine like terms: 2.449489743 + -10 = -7.550510257 g = -7.550510257 Simplifying g = -7.550510257Subproblem 2
g + 10 = -2.449489743 Simplifying g + 10 = -2.449489743 Reorder the terms: 10 + g = -2.449489743 Solving 10 + g = -2.449489743 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 = -2.449489743 + -10 Combine like terms: 10 + -10 = 0 0 + g = -2.449489743 + -10 g = -2.449489743 + -10 Combine like terms: -2.449489743 + -10 = -12.449489743 g = -12.449489743 Simplifying g = -12.449489743Solution
The solution to the problem is based on the solutions from the subproblems. g = {-7.550510257, -12.449489743}
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