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Simplifying g2 + 7g + 12.25 = 0 Reorder the terms: 12.25 + 7g + g2 = 0 Solving 12.25 + 7g + g2 = 0 Solving for variable 'g'. Begin completing the square. Move the constant term to the right: Add '-12.25' to each side of the equation. 12.25 + 7g + -12.25 + g2 = 0 + -12.25 Reorder the terms: 12.25 + -12.25 + 7g + g2 = 0 + -12.25 Combine like terms: 12.25 + -12.25 = 0.00 0.00 + 7g + g2 = 0 + -12.25 7g + g2 = 0 + -12.25 Combine like terms: 0 + -12.25 = -12.25 7g + g2 = -12.25 The g term is 7g. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7g + 12.25 + g2 = -12.25 + 12.25 Reorder the terms: 12.25 + 7g + g2 = -12.25 + 12.25 Combine like terms: -12.25 + 12.25 = 0.00 12.25 + 7g + g2 = 0.00 Factor a perfect square on the left side: (g + 3.5)(g + 3.5) = 0.00 Calculate the square root of the right side: 0.00 Break this problem into two subproblems by setting (g + 3.5) equal to 0.00 and 0.00.Subproblem 1
g + 3.5 = 0.00 Simplifying g + 3.5 = 0.00 Reorder the terms: 3.5 + g = 0.00 Solving 3.5 + g = 0.00 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + g = 0.00 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + g = 0.00 + -3.5 g = 0.00 + -3.5 Combine like terms: 0.00 + -3.5 = -3.5 g = -3.5 Simplifying g = -3.5Subproblem 2
g + 3.5 = 0.00 Simplifying g + 3.5 = 0.00 Reorder the terms: 3.5 + g = 0.00 Solving 3.5 + g = 0.00 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + g = 0.00 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + g = 0.00 + -3.5 g = 0.00 + -3.5 Combine like terms: 0.00 + -3.5 = -3.5 g = -3.5 Simplifying g = -3.5Solution
The solution to the problem is based on the solutions from the subproblems. g = {-3.5, -3.5}
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