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Simplifying 0.5g2 + 8g = -7 Reorder the terms: 8g + 0.5g2 = -7 Solving 8g + 0.5g2 = -7 Solving for variable 'g'. Reorder the terms: 7 + 8g + 0.5g2 = -7 + 7 Combine like terms: -7 + 7 = 0 7 + 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'. 14 + 16g + g2 = 0 Move the constant term to the right: Add '-14' to each side of the equation. 14 + 16g + -14 + g2 = 0 + -14 Reorder the terms: 14 + -14 + 16g + g2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + 16g + g2 = 0 + -14 16g + g2 = 0 + -14 Combine like terms: 0 + -14 = -14 16g + g2 = -14 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 = -14 + 64 Reorder the terms: 64 + 16g + g2 = -14 + 64 Combine like terms: -14 + 64 = 50 64 + 16g + g2 = 50 Factor a perfect square on the left side: (g + 8)(g + 8) = 50 Calculate the square root of the right side: 7.071067812 Break this problem into two subproblems by setting (g + 8) equal to 7.071067812 and -7.071067812.Subproblem 1
g + 8 = 7.071067812 Simplifying g + 8 = 7.071067812 Reorder the terms: 8 + g = 7.071067812 Solving 8 + g = 7.071067812 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 = 7.071067812 + -8 Combine like terms: 8 + -8 = 0 0 + g = 7.071067812 + -8 g = 7.071067812 + -8 Combine like terms: 7.071067812 + -8 = -0.928932188 g = -0.928932188 Simplifying g = -0.928932188Subproblem 2
g + 8 = -7.071067812 Simplifying g + 8 = -7.071067812 Reorder the terms: 8 + g = -7.071067812 Solving 8 + g = -7.071067812 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 = -7.071067812 + -8 Combine like terms: 8 + -8 = 0 0 + g = -7.071067812 + -8 g = -7.071067812 + -8 Combine like terms: -7.071067812 + -8 = -15.071067812 g = -15.071067812 Simplifying g = -15.071067812Solution
The solution to the problem is based on the solutions from the subproblems. g = {-0.928932188, -15.071067812}
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