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Simplifying g2 + -28g + 43 = 0 Reorder the terms: 43 + -28g + g2 = 0 Solving 43 + -28g + g2 = 0 Solving for variable 'g'. Begin completing the square. Move the constant term to the right: Add '-43' to each side of the equation. 43 + -28g + -43 + g2 = 0 + -43 Reorder the terms: 43 + -43 + -28g + g2 = 0 + -43 Combine like terms: 43 + -43 = 0 0 + -28g + g2 = 0 + -43 -28g + g2 = 0 + -43 Combine like terms: 0 + -43 = -43 -28g + g2 = -43 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 = -43 + 196 Reorder the terms: 196 + -28g + g2 = -43 + 196 Combine like terms: -43 + 196 = 153 196 + -28g + g2 = 153 Factor a perfect square on the left side: (g + -14)(g + -14) = 153 Calculate the square root of the right side: 12.369316877 Break this problem into two subproblems by setting (g + -14) equal to 12.369316877 and -12.369316877.Subproblem 1
g + -14 = 12.369316877 Simplifying g + -14 = 12.369316877 Reorder the terms: -14 + g = 12.369316877 Solving -14 + g = 12.369316877 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 = 12.369316877 + 14 Combine like terms: -14 + 14 = 0 0 + g = 12.369316877 + 14 g = 12.369316877 + 14 Combine like terms: 12.369316877 + 14 = 26.369316877 g = 26.369316877 Simplifying g = 26.369316877Subproblem 2
g + -14 = -12.369316877 Simplifying g + -14 = -12.369316877 Reorder the terms: -14 + g = -12.369316877 Solving -14 + g = -12.369316877 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 = -12.369316877 + 14 Combine like terms: -14 + 14 = 0 0 + g = -12.369316877 + 14 g = -12.369316877 + 14 Combine like terms: -12.369316877 + 14 = 1.630683123 g = 1.630683123 Simplifying g = 1.630683123Solution
The solution to the problem is based on the solutions from the subproblems. g = {26.369316877, 1.630683123}
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