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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 = 7.830951895 g = 7.830951895 Simplifying g = 7.830951895Subproblem 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 = -3.830951895 g = -3.830951895 Simplifying g = -3.830951895Solution
The solution to the problem is based on the solutions from the subproblems. g = {7.830951895, -3.830951895}
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