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Simplifying 0.7g2 + -28g + 12000 = 13014.3 Reorder the terms: 12000 + -28g + 0.7g2 = 13014.3 Solving 12000 + -28g + 0.7g2 = 13014.3 Solving for variable 'g'. Reorder the terms: 12000 + -13014.3 + -28g + 0.7g2 = 13014.3 + -13014.3 Combine like terms: 12000 + -13014.3 = -1014.3 -1014.3 + -28g + 0.7g2 = 13014.3 + -13014.3 Combine like terms: 13014.3 + -13014.3 = 0.0 -1014.3 + -28g + 0.7g2 = 0.0 Begin completing the square. Divide all terms by 0.7 the coefficient of the squared term: Divide each side by '0.7'. -1449 + -40g + g2 = 0 Move the constant term to the right: Add '1449' to each side of the equation. -1449 + -40g + 1449 + g2 = 0 + 1449 Reorder the terms: -1449 + 1449 + -40g + g2 = 0 + 1449 Combine like terms: -1449 + 1449 = 0 0 + -40g + g2 = 0 + 1449 -40g + g2 = 0 + 1449 Combine like terms: 0 + 1449 = 1449 -40g + g2 = 1449 The g term is -40g. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40g + 400 + g2 = 1449 + 400 Reorder the terms: 400 + -40g + g2 = 1449 + 400 Combine like terms: 1449 + 400 = 1849 400 + -40g + g2 = 1849 Factor a perfect square on the left side: (g + -20)(g + -20) = 1849 Calculate the square root of the right side: 43 Break this problem into two subproblems by setting (g + -20) equal to 43 and -43.Subproblem 1
g + -20 = 43 Simplifying g + -20 = 43 Reorder the terms: -20 + g = 43 Solving -20 + g = 43 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + g = 43 + 20 Combine like terms: -20 + 20 = 0 0 + g = 43 + 20 g = 43 + 20 Combine like terms: 43 + 20 = 63 g = 63 Simplifying g = 63Subproblem 2
g + -20 = -43 Simplifying g + -20 = -43 Reorder the terms: -20 + g = -43 Solving -20 + g = -43 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + g = -43 + 20 Combine like terms: -20 + 20 = 0 0 + g = -43 + 20 g = -43 + 20 Combine like terms: -43 + 20 = -23 g = -23 Simplifying g = -23Solution
The solution to the problem is based on the solutions from the subproblems. g = {63, -23}
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