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Simplifying 2g2 + -14g + -220 = 0 Reorder the terms: -220 + -14g + 2g2 = 0 Solving -220 + -14g + 2g2 = 0 Solving for variable 'g'. Factor out the Greatest Common Factor (GCF), '2'. 2(-110 + -7g + g2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-110 + -7g + g2)' equal to zero and attempt to solve: Simplifying -110 + -7g + g2 = 0 Solving -110 + -7g + g2 = 0 Begin completing the square. Move the constant term to the right: Add '110' to each side of the equation. -110 + -7g + 110 + g2 = 0 + 110 Reorder the terms: -110 + 110 + -7g + g2 = 0 + 110 Combine like terms: -110 + 110 = 0 0 + -7g + g2 = 0 + 110 -7g + g2 = 0 + 110 Combine like terms: 0 + 110 = 110 -7g + g2 = 110 The g term is -7g. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7g + 12.25 + g2 = 110 + 12.25 Reorder the terms: 12.25 + -7g + g2 = 110 + 12.25 Combine like terms: 110 + 12.25 = 122.25 12.25 + -7g + g2 = 122.25 Factor a perfect square on the left side: (g + -3.5)(g + -3.5) = 122.25 Calculate the square root of the right side: 11.056672194 Break this problem into two subproblems by setting (g + -3.5) equal to 11.056672194 and -11.056672194.Subproblem 1
g + -3.5 = 11.056672194 Simplifying g + -3.5 = 11.056672194 Reorder the terms: -3.5 + g = 11.056672194 Solving -3.5 + g = 11.056672194 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + g = 11.056672194 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + g = 11.056672194 + 3.5 g = 11.056672194 + 3.5 Combine like terms: 11.056672194 + 3.5 = 14.556672194 g = 14.556672194 Simplifying g = 14.556672194Subproblem 2
g + -3.5 = -11.056672194 Simplifying g + -3.5 = -11.056672194 Reorder the terms: -3.5 + g = -11.056672194 Solving -3.5 + g = -11.056672194 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + g = -11.056672194 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + g = -11.056672194 + 3.5 g = -11.056672194 + 3.5 Combine like terms: -11.056672194 + 3.5 = -7.556672194 g = -7.556672194 Simplifying g = -7.556672194Solution
The solution to the problem is based on the solutions from the subproblems. g = {14.556672194, -7.556672194}Solution
g = {14.556672194, -7.556672194}
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