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Simplifying 16g2 + 24g = 9 Reorder the terms: 24g + 16g2 = 9 Solving 24g + 16g2 = 9 Solving for variable 'g'. Reorder the terms: -9 + 24g + 16g2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + 24g + 16g2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.5625 + 1.5g + g2 = 0 Move the constant term to the right: Add '0.5625' to each side of the equation. -0.5625 + 1.5g + 0.5625 + g2 = 0 + 0.5625 Reorder the terms: -0.5625 + 0.5625 + 1.5g + g2 = 0 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + 1.5g + g2 = 0 + 0.5625 1.5g + g2 = 0 + 0.5625 Combine like terms: 0 + 0.5625 = 0.5625 1.5g + g2 = 0.5625 The g term is 1.5g. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5g + 0.5625 + g2 = 0.5625 + 0.5625 Reorder the terms: 0.5625 + 1.5g + g2 = 0.5625 + 0.5625 Combine like terms: 0.5625 + 0.5625 = 1.125 0.5625 + 1.5g + g2 = 1.125 Factor a perfect square on the left side: (g + 0.75)(g + 0.75) = 1.125 Calculate the square root of the right side: 1.060660172 Break this problem into two subproblems by setting (g + 0.75) equal to 1.060660172 and -1.060660172.Subproblem 1
g + 0.75 = 1.060660172 Simplifying g + 0.75 = 1.060660172 Reorder the terms: 0.75 + g = 1.060660172 Solving 0.75 + g = 1.060660172 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + g = 1.060660172 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + g = 1.060660172 + -0.75 g = 1.060660172 + -0.75 Combine like terms: 1.060660172 + -0.75 = 0.310660172 g = 0.310660172 Simplifying g = 0.310660172Subproblem 2
g + 0.75 = -1.060660172 Simplifying g + 0.75 = -1.060660172 Reorder the terms: 0.75 + g = -1.060660172 Solving 0.75 + g = -1.060660172 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + g = -1.060660172 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + g = -1.060660172 + -0.75 g = -1.060660172 + -0.75 Combine like terms: -1.060660172 + -0.75 = -1.810660172 g = -1.810660172 Simplifying g = -1.810660172Solution
The solution to the problem is based on the solutions from the subproblems. g = {0.310660172, -1.810660172}
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