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Simplifying -5g(8 + -1g) = 12 (8 * -5g + -1g * -5g) = 12 (-40g + 5g2) = 12 Solving -40g + 5g2 = 12 Solving for variable 'g'. Reorder the terms: -12 + -40g + 5g2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + -40g + 5g2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.4 + -8g + g2 = 0 Move the constant term to the right: Add '2.4' to each side of the equation. -2.4 + -8g + 2.4 + g2 = 0 + 2.4 Reorder the terms: -2.4 + 2.4 + -8g + g2 = 0 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + -8g + g2 = 0 + 2.4 -8g + g2 = 0 + 2.4 Combine like terms: 0 + 2.4 = 2.4 -8g + g2 = 2.4 The g term is -8g. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8g + 16 + g2 = 2.4 + 16 Reorder the terms: 16 + -8g + g2 = 2.4 + 16 Combine like terms: 2.4 + 16 = 18.4 16 + -8g + g2 = 18.4 Factor a perfect square on the left side: (g + -4)(g + -4) = 18.4 Calculate the square root of the right side: 4.289522118 Break this problem into two subproblems by setting (g + -4) equal to 4.289522118 and -4.289522118.Subproblem 1
g + -4 = 4.289522118 Simplifying g + -4 = 4.289522118 Reorder the terms: -4 + g = 4.289522118 Solving -4 + g = 4.289522118 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + g = 4.289522118 + 4 Combine like terms: -4 + 4 = 0 0 + g = 4.289522118 + 4 g = 4.289522118 + 4 Combine like terms: 4.289522118 + 4 = 8.289522118 g = 8.289522118 Simplifying g = 8.289522118Subproblem 2
g + -4 = -4.289522118 Simplifying g + -4 = -4.289522118 Reorder the terms: -4 + g = -4.289522118 Solving -4 + g = -4.289522118 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + g = -4.289522118 + 4 Combine like terms: -4 + 4 = 0 0 + g = -4.289522118 + 4 g = -4.289522118 + 4 Combine like terms: -4.289522118 + 4 = -0.289522118 g = -0.289522118 Simplifying g = -0.289522118Solution
The solution to the problem is based on the solutions from the subproblems. g = {8.289522118, -0.289522118}
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