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Simplifying -5g(-8 + g) = 12 (-8 * -5g + g * -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 = 13.6 16 + -8g + g2 = 13.6 Factor a perfect square on the left side: (g + -4)(g + -4) = 13.6 Calculate the square root of the right side: 3.687817783 Break this problem into two subproblems by setting (g + -4) equal to 3.687817783 and -3.687817783.Subproblem 1
g + -4 = 3.687817783 Simplifying g + -4 = 3.687817783 Reorder the terms: -4 + g = 3.687817783 Solving -4 + g = 3.687817783 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 = 3.687817783 + 4 Combine like terms: -4 + 4 = 0 0 + g = 3.687817783 + 4 g = 3.687817783 + 4 Combine like terms: 3.687817783 + 4 = 7.687817783 g = 7.687817783 Simplifying g = 7.687817783Subproblem 2
g + -4 = -3.687817783 Simplifying g + -4 = -3.687817783 Reorder the terms: -4 + g = -3.687817783 Solving -4 + g = -3.687817783 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 = -3.687817783 + 4 Combine like terms: -4 + 4 = 0 0 + g = -3.687817783 + 4 g = -3.687817783 + 4 Combine like terms: -3.687817783 + 4 = 0.312182217 g = 0.312182217 Simplifying g = 0.312182217Solution
The solution to the problem is based on the solutions from the subproblems. g = {7.687817783, 0.312182217}
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