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Simplifying g2 + 7g + -1260 = 0 Reorder the terms: -1260 + 7g + g2 = 0 Solving -1260 + 7g + g2 = 0 Solving for variable 'g'. Begin completing the square. Move the constant term to the right: Add '1260' to each side of the equation. -1260 + 7g + 1260 + g2 = 0 + 1260 Reorder the terms: -1260 + 1260 + 7g + g2 = 0 + 1260 Combine like terms: -1260 + 1260 = 0 0 + 7g + g2 = 0 + 1260 7g + g2 = 0 + 1260 Combine like terms: 0 + 1260 = 1260 7g + g2 = 1260 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 = 1260 + 12.25 Reorder the terms: 12.25 + 7g + g2 = 1260 + 12.25 Combine like terms: 1260 + 12.25 = 1272.25 12.25 + 7g + g2 = 1272.25 Factor a perfect square on the left side: (g + 3.5)(g + 3.5) = 1272.25 Calculate the square root of the right side: 35.668613654 Break this problem into two subproblems by setting (g + 3.5) equal to 35.668613654 and -35.668613654.Subproblem 1
g + 3.5 = 35.668613654 Simplifying g + 3.5 = 35.668613654 Reorder the terms: 3.5 + g = 35.668613654 Solving 3.5 + g = 35.668613654 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 = 35.668613654 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + g = 35.668613654 + -3.5 g = 35.668613654 + -3.5 Combine like terms: 35.668613654 + -3.5 = 32.168613654 g = 32.168613654 Simplifying g = 32.168613654Subproblem 2
g + 3.5 = -35.668613654 Simplifying g + 3.5 = -35.668613654 Reorder the terms: 3.5 + g = -35.668613654 Solving 3.5 + g = -35.668613654 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 = -35.668613654 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + g = -35.668613654 + -3.5 g = -35.668613654 + -3.5 Combine like terms: -35.668613654 + -3.5 = -39.168613654 g = -39.168613654 Simplifying g = -39.168613654Solution
The solution to the problem is based on the solutions from the subproblems. g = {32.168613654, -39.168613654}
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