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Simplifying g2 + -20g = -49 Reorder the terms: -20g + g2 = -49 Solving -20g + g2 = -49 Solving for variable 'g'. Reorder the terms: 49 + -20g + g2 = -49 + 49 Combine like terms: -49 + 49 = 0 49 + -20g + g2 = 0 Begin completing the square. Move the constant term to the right: Add '-49' to each side of the equation. 49 + -20g + -49 + g2 = 0 + -49 Reorder the terms: 49 + -49 + -20g + g2 = 0 + -49 Combine like terms: 49 + -49 = 0 0 + -20g + g2 = 0 + -49 -20g + g2 = 0 + -49 Combine like terms: 0 + -49 = -49 -20g + g2 = -49 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 = -49 + 100 Reorder the terms: 100 + -20g + g2 = -49 + 100 Combine like terms: -49 + 100 = 51 100 + -20g + g2 = 51 Factor a perfect square on the left side: (g + -10)(g + -10) = 51 Calculate the square root of the right side: 7.141428429 Break this problem into two subproblems by setting (g + -10) equal to 7.141428429 and -7.141428429.Subproblem 1
g + -10 = 7.141428429 Simplifying g + -10 = 7.141428429 Reorder the terms: -10 + g = 7.141428429 Solving -10 + g = 7.141428429 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 = 7.141428429 + 10 Combine like terms: -10 + 10 = 0 0 + g = 7.141428429 + 10 g = 7.141428429 + 10 Combine like terms: 7.141428429 + 10 = 17.141428429 g = 17.141428429 Simplifying g = 17.141428429Subproblem 2
g + -10 = -7.141428429 Simplifying g + -10 = -7.141428429 Reorder the terms: -10 + g = -7.141428429 Solving -10 + g = -7.141428429 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 = -7.141428429 + 10 Combine like terms: -10 + 10 = 0 0 + g = -7.141428429 + 10 g = -7.141428429 + 10 Combine like terms: -7.141428429 + 10 = 2.858571571 g = 2.858571571 Simplifying g = 2.858571571Solution
The solution to the problem is based on the solutions from the subproblems. g = {17.141428429, 2.858571571}
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