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Simplifying 360 = (3g + 40) * 4g Reorder the terms: 360 = (40 + 3g) * 4g Reorder the terms for easier multiplication: 360 = 4g(40 + 3g) 360 = (40 * 4g + 3g * 4g) 360 = (160g + 12g2) Solving 360 = 160g + 12g2 Solving for variable 'g'. Reorder the terms: 360 + -160g + -12g2 = 160g + -160g + 12g2 + -12g2 Combine like terms: 160g + -160g = 0 360 + -160g + -12g2 = 0 + 12g2 + -12g2 360 + -160g + -12g2 = 12g2 + -12g2 Combine like terms: 12g2 + -12g2 = 0 360 + -160g + -12g2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(90 + -40g + -3g2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(90 + -40g + -3g2)' equal to zero and attempt to solve: Simplifying 90 + -40g + -3g2 = 0 Solving 90 + -40g + -3g2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -30 + 13.33333333g + g2 = 0 Move the constant term to the right: Add '30' to each side of the equation. -30 + 13.33333333g + 30 + g2 = 0 + 30 Reorder the terms: -30 + 30 + 13.33333333g + g2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + 13.33333333g + g2 = 0 + 30 13.33333333g + g2 = 0 + 30 Combine like terms: 0 + 30 = 30 13.33333333g + g2 = 30 The g term is 13.33333333g. Take half its coefficient (6.666666665). Square it (44.44444442) and add it to both sides. Add '44.44444442' to each side of the equation. 13.33333333g + 44.44444442 + g2 = 30 + 44.44444442 Reorder the terms: 44.44444442 + 13.33333333g + g2 = 30 + 44.44444442 Combine like terms: 30 + 44.44444442 = 74.44444442 44.44444442 + 13.33333333g + g2 = 74.44444442 Factor a perfect square on the left side: (g + 6.666666665)(g + 6.666666665) = 74.44444442 Calculate the square root of the right side: 8.628119402 Break this problem into two subproblems by setting (g + 6.666666665) equal to 8.628119402 and -8.628119402.Subproblem 1
g + 6.666666665 = 8.628119402 Simplifying g + 6.666666665 = 8.628119402 Reorder the terms: 6.666666665 + g = 8.628119402 Solving 6.666666665 + g = 8.628119402 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-6.666666665' to each side of the equation. 6.666666665 + -6.666666665 + g = 8.628119402 + -6.666666665 Combine like terms: 6.666666665 + -6.666666665 = 0.000000000 0.000000000 + g = 8.628119402 + -6.666666665 g = 8.628119402 + -6.666666665 Combine like terms: 8.628119402 + -6.666666665 = 1.961452737 g = 1.961452737 Simplifying g = 1.961452737Subproblem 2
g + 6.666666665 = -8.628119402 Simplifying g + 6.666666665 = -8.628119402 Reorder the terms: 6.666666665 + g = -8.628119402 Solving 6.666666665 + g = -8.628119402 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-6.666666665' to each side of the equation. 6.666666665 + -6.666666665 + g = -8.628119402 + -6.666666665 Combine like terms: 6.666666665 + -6.666666665 = 0.000000000 0.000000000 + g = -8.628119402 + -6.666666665 g = -8.628119402 + -6.666666665 Combine like terms: -8.628119402 + -6.666666665 = -15.294786067 g = -15.294786067 Simplifying g = -15.294786067Solution
The solution to the problem is based on the solutions from the subproblems. g = {1.961452737, -15.294786067}Solution
g = {1.961452737, -15.294786067}
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