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Simplifying g2 + 7g = 288 Reorder the terms: 7g + g2 = 288 Solving 7g + g2 = 288 Solving for variable 'g'. Reorder the terms: -288 + 7g + g2 = 288 + -288 Combine like terms: 288 + -288 = 0 -288 + 7g + g2 = 0 Begin completing the square. Move the constant term to the right: Add '288' to each side of the equation. -288 + 7g + 288 + g2 = 0 + 288 Reorder the terms: -288 + 288 + 7g + g2 = 0 + 288 Combine like terms: -288 + 288 = 0 0 + 7g + g2 = 0 + 288 7g + g2 = 0 + 288 Combine like terms: 0 + 288 = 288 7g + g2 = 288 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 = 288 + 12.25 Reorder the terms: 12.25 + 7g + g2 = 288 + 12.25 Combine like terms: 288 + 12.25 = 300.25 12.25 + 7g + g2 = 300.25 Factor a perfect square on the left side: (g + 3.5)(g + 3.5) = 300.25 Calculate the square root of the right side: 17.327723451 Break this problem into two subproblems by setting (g + 3.5) equal to 17.327723451 and -17.327723451.Subproblem 1
g + 3.5 = 17.327723451 Simplifying g + 3.5 = 17.327723451 Reorder the terms: 3.5 + g = 17.327723451 Solving 3.5 + g = 17.327723451 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 = 17.327723451 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + g = 17.327723451 + -3.5 g = 17.327723451 + -3.5 Combine like terms: 17.327723451 + -3.5 = 13.827723451 g = 13.827723451 Simplifying g = 13.827723451Subproblem 2
g + 3.5 = -17.327723451 Simplifying g + 3.5 = -17.327723451 Reorder the terms: 3.5 + g = -17.327723451 Solving 3.5 + g = -17.327723451 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 = -17.327723451 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + g = -17.327723451 + -3.5 g = -17.327723451 + -3.5 Combine like terms: -17.327723451 + -3.5 = -20.827723451 g = -20.827723451 Simplifying g = -20.827723451Solution
The solution to the problem is based on the solutions from the subproblems. g = {13.827723451, -20.827723451}
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