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Simplifying g2 + 4g + -32 = 9 Reorder the terms: -32 + 4g + g2 = 9 Solving -32 + 4g + g2 = 9 Solving for variable 'g'. Reorder the terms: -32 + -9 + 4g + g2 = 9 + -9 Combine like terms: -32 + -9 = -41 -41 + 4g + g2 = 9 + -9 Combine like terms: 9 + -9 = 0 -41 + 4g + g2 = 0 Begin completing the square. Move the constant term to the right: Add '41' to each side of the equation. -41 + 4g + 41 + g2 = 0 + 41 Reorder the terms: -41 + 41 + 4g + g2 = 0 + 41 Combine like terms: -41 + 41 = 0 0 + 4g + g2 = 0 + 41 4g + g2 = 0 + 41 Combine like terms: 0 + 41 = 41 4g + g2 = 41 The g term is 4g. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4g + 4 + g2 = 41 + 4 Reorder the terms: 4 + 4g + g2 = 41 + 4 Combine like terms: 41 + 4 = 45 4 + 4g + g2 = 45 Factor a perfect square on the left side: (g + 2)(g + 2) = 45 Calculate the square root of the right side: 6.708203933 Break this problem into two subproblems by setting (g + 2) equal to 6.708203933 and -6.708203933.Subproblem 1
g + 2 = 6.708203933 Simplifying g + 2 = 6.708203933 Reorder the terms: 2 + g = 6.708203933 Solving 2 + g = 6.708203933 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + g = 6.708203933 + -2 Combine like terms: 2 + -2 = 0 0 + g = 6.708203933 + -2 g = 6.708203933 + -2 Combine like terms: 6.708203933 + -2 = 4.708203933 g = 4.708203933 Simplifying g = 4.708203933Subproblem 2
g + 2 = -6.708203933 Simplifying g + 2 = -6.708203933 Reorder the terms: 2 + g = -6.708203933 Solving 2 + g = -6.708203933 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + g = -6.708203933 + -2 Combine like terms: 2 + -2 = 0 0 + g = -6.708203933 + -2 g = -6.708203933 + -2 Combine like terms: -6.708203933 + -2 = -8.708203933 g = -8.708203933 Simplifying g = -8.708203933Solution
The solution to the problem is based on the solutions from the subproblems. g = {4.708203933, -8.708203933}
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