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Simplifying g2 + 4g + -30 = 0 Reorder the terms: -30 + 4g + g2 = 0 Solving -30 + 4g + g2 = 0 Solving for variable 'g'. Begin completing the square. Move the constant term to the right: Add '30' to each side of the equation. -30 + 4g + 30 + g2 = 0 + 30 Reorder the terms: -30 + 30 + 4g + g2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + 4g + g2 = 0 + 30 4g + g2 = 0 + 30 Combine like terms: 0 + 30 = 30 4g + g2 = 30 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 = 30 + 4 Reorder the terms: 4 + 4g + g2 = 30 + 4 Combine like terms: 30 + 4 = 34 4 + 4g + g2 = 34 Factor a perfect square on the left side: (g + 2)(g + 2) = 34 Calculate the square root of the right side: 5.830951895 Break this problem into two subproblems by setting (g + 2) equal to 5.830951895 and -5.830951895.Subproblem 1
g + 2 = 5.830951895 Simplifying g + 2 = 5.830951895 Reorder the terms: 2 + g = 5.830951895 Solving 2 + g = 5.830951895 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 = 5.830951895 + -2 Combine like terms: 2 + -2 = 0 0 + g = 5.830951895 + -2 g = 5.830951895 + -2 Combine like terms: 5.830951895 + -2 = 3.830951895 g = 3.830951895 Simplifying g = 3.830951895Subproblem 2
g + 2 = -5.830951895 Simplifying g + 2 = -5.830951895 Reorder the terms: 2 + g = -5.830951895 Solving 2 + g = -5.830951895 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 = -5.830951895 + -2 Combine like terms: 2 + -2 = 0 0 + g = -5.830951895 + -2 g = -5.830951895 + -2 Combine like terms: -5.830951895 + -2 = -7.830951895 g = -7.830951895 Simplifying g = -7.830951895Solution
The solution to the problem is based on the solutions from the subproblems. g = {3.830951895, -7.830951895}
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