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Simplifying -4g2 + 112g + 100 = 0 Reorder the terms: 100 + 112g + -4g2 = 0 Solving 100 + 112g + -4g2 = 0 Solving for variable 'g'. Factor out the Greatest Common Factor (GCF), '4'. 4(25 + 28g + -1g2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(25 + 28g + -1g2)' equal to zero and attempt to solve: Simplifying 25 + 28g + -1g2 = 0 Solving 25 + 28g + -1g2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -25 + -28g + g2 = 0 Move the constant term to the right: Add '25' to each side of the equation. -25 + -28g + 25 + g2 = 0 + 25 Reorder the terms: -25 + 25 + -28g + g2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -28g + g2 = 0 + 25 -28g + g2 = 0 + 25 Combine like terms: 0 + 25 = 25 -28g + g2 = 25 The g term is -28g. Take half its coefficient (-14). Square it (196) and add it to both sides. Add '196' to each side of the equation. -28g + 196 + g2 = 25 + 196 Reorder the terms: 196 + -28g + g2 = 25 + 196 Combine like terms: 25 + 196 = 221 196 + -28g + g2 = 221 Factor a perfect square on the left side: (g + -14)(g + -14) = 221 Calculate the square root of the right side: 14.866068747 Break this problem into two subproblems by setting (g + -14) equal to 14.866068747 and -14.866068747.Subproblem 1
g + -14 = 14.866068747 Simplifying g + -14 = 14.866068747 Reorder the terms: -14 + g = 14.866068747 Solving -14 + g = 14.866068747 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + g = 14.866068747 + 14 Combine like terms: -14 + 14 = 0 0 + g = 14.866068747 + 14 g = 14.866068747 + 14 Combine like terms: 14.866068747 + 14 = 28.866068747 g = 28.866068747 Simplifying g = 28.866068747Subproblem 2
g + -14 = -14.866068747 Simplifying g + -14 = -14.866068747 Reorder the terms: -14 + g = -14.866068747 Solving -14 + g = -14.866068747 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + g = -14.866068747 + 14 Combine like terms: -14 + 14 = 0 0 + g = -14.866068747 + 14 g = -14.866068747 + 14 Combine like terms: -14.866068747 + 14 = -0.866068747 g = -0.866068747 Simplifying g = -0.866068747Solution
The solution to the problem is based on the solutions from the subproblems. g = {28.866068747, -0.866068747}Solution
g = {28.866068747, -0.866068747}
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