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Simplifying 0.5g2 + 8g + 16 = -7 Reorder the terms: 16 + 8g + 0.5g2 = -7 Solving 16 + 8g + 0.5g2 = -7 Solving for variable 'g'. Reorder the terms: 16 + 7 + 8g + 0.5g2 = -7 + 7 Combine like terms: 16 + 7 = 23 23 + 8g + 0.5g2 = -7 + 7 Combine like terms: -7 + 7 = 0 23 + 8g + 0.5g2 = 0 Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. 46 + 16g + g2 = 0 Move the constant term to the right: Add '-46' to each side of the equation. 46 + 16g + -46 + g2 = 0 + -46 Reorder the terms: 46 + -46 + 16g + g2 = 0 + -46 Combine like terms: 46 + -46 = 0 0 + 16g + g2 = 0 + -46 16g + g2 = 0 + -46 Combine like terms: 0 + -46 = -46 16g + g2 = -46 The g term is 16g. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16g + 64 + g2 = -46 + 64 Reorder the terms: 64 + 16g + g2 = -46 + 64 Combine like terms: -46 + 64 = 18 64 + 16g + g2 = 18 Factor a perfect square on the left side: (g + 8)(g + 8) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (g + 8) equal to 4.242640687 and -4.242640687.Subproblem 1
g + 8 = 4.242640687 Simplifying g + 8 = 4.242640687 Reorder the terms: 8 + g = 4.242640687 Solving 8 + g = 4.242640687 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + g = 4.242640687 + -8 Combine like terms: 8 + -8 = 0 0 + g = 4.242640687 + -8 g = 4.242640687 + -8 Combine like terms: 4.242640687 + -8 = -3.757359313 g = -3.757359313 Simplifying g = -3.757359313Subproblem 2
g + 8 = -4.242640687 Simplifying g + 8 = -4.242640687 Reorder the terms: 8 + g = -4.242640687 Solving 8 + g = -4.242640687 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + g = -4.242640687 + -8 Combine like terms: 8 + -8 = 0 0 + g = -4.242640687 + -8 g = -4.242640687 + -8 Combine like terms: -4.242640687 + -8 = -12.242640687 g = -12.242640687 Simplifying g = -12.242640687Solution
The solution to the problem is based on the solutions from the subproblems. g = {-3.757359313, -12.242640687}
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