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Simplifying 3g2 + -84g + 15 = 0 Reorder the terms: 15 + -84g + 3g2 = 0 Solving 15 + -84g + 3g2 = 0 Solving for variable 'g'. Factor out the Greatest Common Factor (GCF), '3'. 3(5 + -28g + g2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(5 + -28g + g2)' equal to zero and attempt to solve: Simplifying 5 + -28g + g2 = 0 Solving 5 + -28g + g2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + -28g + -5 + g2 = 0 + -5 Reorder the terms: 5 + -5 + -28g + g2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -28g + g2 = 0 + -5 -28g + g2 = 0 + -5 Combine like terms: 0 + -5 = -5 -28g + g2 = -5 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 = -5 + 196 Reorder the terms: 196 + -28g + g2 = -5 + 196 Combine like terms: -5 + 196 = 191 196 + -28g + g2 = 191 Factor a perfect square on the left side: (g + -14)(g + -14) = 191 Calculate the square root of the right side: 13.820274961 Break this problem into two subproblems by setting (g + -14) equal to 13.820274961 and -13.820274961.Subproblem 1
g + -14 = 13.820274961 Simplifying g + -14 = 13.820274961 Reorder the terms: -14 + g = 13.820274961 Solving -14 + g = 13.820274961 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 = 13.820274961 + 14 Combine like terms: -14 + 14 = 0 0 + g = 13.820274961 + 14 g = 13.820274961 + 14 Combine like terms: 13.820274961 + 14 = 27.820274961 g = 27.820274961 Simplifying g = 27.820274961Subproblem 2
g + -14 = -13.820274961 Simplifying g + -14 = -13.820274961 Reorder the terms: -14 + g = -13.820274961 Solving -14 + g = -13.820274961 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 = -13.820274961 + 14 Combine like terms: -14 + 14 = 0 0 + g = -13.820274961 + 14 g = -13.820274961 + 14 Combine like terms: -13.820274961 + 14 = 0.179725039 g = 0.179725039 Simplifying g = 0.179725039Solution
The solution to the problem is based on the solutions from the subproblems. g = {27.820274961, 0.179725039}Solution
g = {27.820274961, 0.179725039}
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