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Simplifying g2 + 4g = 13 Reorder the terms: 4g + g2 = 13 Solving 4g + g2 = 13 Solving for variable 'g'. Reorder the terms: -13 + 4g + g2 = 13 + -13 Combine like terms: 13 + -13 = 0 -13 + 4g + g2 = 0 Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + 4g + 13 + g2 = 0 + 13 Reorder the terms: -13 + 13 + 4g + g2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 4g + g2 = 0 + 13 4g + g2 = 0 + 13 Combine like terms: 0 + 13 = 13 4g + g2 = 13 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 = 13 + 4 Reorder the terms: 4 + 4g + g2 = 13 + 4 Combine like terms: 13 + 4 = 17 4 + 4g + g2 = 17 Factor a perfect square on the left side: (g + 2)(g + 2) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (g + 2) equal to 4.123105626 and -4.123105626.Subproblem 1
g + 2 = 4.123105626 Simplifying g + 2 = 4.123105626 Reorder the terms: 2 + g = 4.123105626 Solving 2 + g = 4.123105626 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 = 4.123105626 + -2 Combine like terms: 2 + -2 = 0 0 + g = 4.123105626 + -2 g = 4.123105626 + -2 Combine like terms: 4.123105626 + -2 = 2.123105626 g = 2.123105626 Simplifying g = 2.123105626Subproblem 2
g + 2 = -4.123105626 Simplifying g + 2 = -4.123105626 Reorder the terms: 2 + g = -4.123105626 Solving 2 + g = -4.123105626 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 = -4.123105626 + -2 Combine like terms: 2 + -2 = 0 0 + g = -4.123105626 + -2 g = -4.123105626 + -2 Combine like terms: -4.123105626 + -2 = -6.123105626 g = -6.123105626 Simplifying g = -6.123105626Solution
The solution to the problem is based on the solutions from the subproblems. g = {2.123105626, -6.123105626}
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