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Simplifying 4g2 + 20g = 124 Reorder the terms: 20g + 4g2 = 124 Solving 20g + 4g2 = 124 Solving for variable 'g'. Reorder the terms: -124 + 20g + 4g2 = 124 + -124 Combine like terms: 124 + -124 = 0 -124 + 20g + 4g2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-31 + 5g + g2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-31 + 5g + g2)' equal to zero and attempt to solve: Simplifying -31 + 5g + g2 = 0 Solving -31 + 5g + g2 = 0 Begin completing the square. Move the constant term to the right: Add '31' to each side of the equation. -31 + 5g + 31 + g2 = 0 + 31 Reorder the terms: -31 + 31 + 5g + g2 = 0 + 31 Combine like terms: -31 + 31 = 0 0 + 5g + g2 = 0 + 31 5g + g2 = 0 + 31 Combine like terms: 0 + 31 = 31 5g + g2 = 31 The g term is 5g. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5g + 6.25 + g2 = 31 + 6.25 Reorder the terms: 6.25 + 5g + g2 = 31 + 6.25 Combine like terms: 31 + 6.25 = 37.25 6.25 + 5g + g2 = 37.25 Factor a perfect square on the left side: (g + 2.5)(g + 2.5) = 37.25 Calculate the square root of the right side: 6.103277808 Break this problem into two subproblems by setting (g + 2.5) equal to 6.103277808 and -6.103277808.Subproblem 1
g + 2.5 = 6.103277808 Simplifying g + 2.5 = 6.103277808 Reorder the terms: 2.5 + g = 6.103277808 Solving 2.5 + g = 6.103277808 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + g = 6.103277808 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + g = 6.103277808 + -2.5 g = 6.103277808 + -2.5 Combine like terms: 6.103277808 + -2.5 = 3.603277808 g = 3.603277808 Simplifying g = 3.603277808Subproblem 2
g + 2.5 = -6.103277808 Simplifying g + 2.5 = -6.103277808 Reorder the terms: 2.5 + g = -6.103277808 Solving 2.5 + g = -6.103277808 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + g = -6.103277808 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + g = -6.103277808 + -2.5 g = -6.103277808 + -2.5 Combine like terms: -6.103277808 + -2.5 = -8.603277808 g = -8.603277808 Simplifying g = -8.603277808Solution
The solution to the problem is based on the solutions from the subproblems. g = {3.603277808, -8.603277808}Solution
g = {3.603277808, -8.603277808}
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