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Simplifying g2 + 26g = 47 Reorder the terms: 26g + g2 = 47 Solving 26g + g2 = 47 Solving for variable 'g'. Reorder the terms: -47 + 26g + g2 = 47 + -47 Combine like terms: 47 + -47 = 0 -47 + 26g + g2 = 0 Begin completing the square. Move the constant term to the right: Add '47' to each side of the equation. -47 + 26g + 47 + g2 = 0 + 47 Reorder the terms: -47 + 47 + 26g + g2 = 0 + 47 Combine like terms: -47 + 47 = 0 0 + 26g + g2 = 0 + 47 26g + g2 = 0 + 47 Combine like terms: 0 + 47 = 47 26g + g2 = 47 The g term is 26g. Take half its coefficient (13). Square it (169) and add it to both sides. Add '169' to each side of the equation. 26g + 169 + g2 = 47 + 169 Reorder the terms: 169 + 26g + g2 = 47 + 169 Combine like terms: 47 + 169 = 216 169 + 26g + g2 = 216 Factor a perfect square on the left side: (g + 13)(g + 13) = 216 Calculate the square root of the right side: 14.696938457 Break this problem into two subproblems by setting (g + 13) equal to 14.696938457 and -14.696938457.Subproblem 1
g + 13 = 14.696938457 Simplifying g + 13 = 14.696938457 Reorder the terms: 13 + g = 14.696938457 Solving 13 + g = 14.696938457 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + g = 14.696938457 + -13 Combine like terms: 13 + -13 = 0 0 + g = 14.696938457 + -13 g = 14.696938457 + -13 Combine like terms: 14.696938457 + -13 = 1.696938457 g = 1.696938457 Simplifying g = 1.696938457Subproblem 2
g + 13 = -14.696938457 Simplifying g + 13 = -14.696938457 Reorder the terms: 13 + g = -14.696938457 Solving 13 + g = -14.696938457 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + g = -14.696938457 + -13 Combine like terms: 13 + -13 = 0 0 + g = -14.696938457 + -13 g = -14.696938457 + -13 Combine like terms: -14.696938457 + -13 = -27.696938457 g = -27.696938457 Simplifying g = -27.696938457Solution
The solution to the problem is based on the solutions from the subproblems. g = {1.696938457, -27.696938457}
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