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Simplifying 2g2 + -12g = -4 Reorder the terms: -12g + 2g2 = -4 Solving -12g + 2g2 = -4 Solving for variable 'g'. Reorder the terms: 4 + -12g + 2g2 = -4 + 4 Combine like terms: -4 + 4 = 0 4 + -12g + 2g2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(2 + -6g + g2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + -6g + g2)' equal to zero and attempt to solve: Simplifying 2 + -6g + g2 = 0 Solving 2 + -6g + g2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + -6g + -2 + g2 = 0 + -2 Reorder the terms: 2 + -2 + -6g + g2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -6g + g2 = 0 + -2 -6g + g2 = 0 + -2 Combine like terms: 0 + -2 = -2 -6g + g2 = -2 The g term is -6g. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6g + 9 + g2 = -2 + 9 Reorder the terms: 9 + -6g + g2 = -2 + 9 Combine like terms: -2 + 9 = 7 9 + -6g + g2 = 7 Factor a perfect square on the left side: (g + -3)(g + -3) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (g + -3) equal to 2.645751311 and -2.645751311.Subproblem 1
g + -3 = 2.645751311 Simplifying g + -3 = 2.645751311 Reorder the terms: -3 + g = 2.645751311 Solving -3 + g = 2.645751311 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + g = 2.645751311 + 3 Combine like terms: -3 + 3 = 0 0 + g = 2.645751311 + 3 g = 2.645751311 + 3 Combine like terms: 2.645751311 + 3 = 5.645751311 g = 5.645751311 Simplifying g = 5.645751311Subproblem 2
g + -3 = -2.645751311 Simplifying g + -3 = -2.645751311 Reorder the terms: -3 + g = -2.645751311 Solving -3 + g = -2.645751311 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + g = -2.645751311 + 3 Combine like terms: -3 + 3 = 0 0 + g = -2.645751311 + 3 g = -2.645751311 + 3 Combine like terms: -2.645751311 + 3 = 0.354248689 g = 0.354248689 Simplifying g = 0.354248689Solution
The solution to the problem is based on the solutions from the subproblems. g = {5.645751311, 0.354248689}Solution
g = {5.645751311, 0.354248689}
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