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Simplifying g2 + 26g + 45 = 0 Reorder the terms: 45 + 26g + g2 = 0 Solving 45 + 26g + g2 = 0 Solving for variable 'g'. Begin completing the square. Move the constant term to the right: Add '-45' to each side of the equation. 45 + 26g + -45 + g2 = 0 + -45 Reorder the terms: 45 + -45 + 26g + g2 = 0 + -45 Combine like terms: 45 + -45 = 0 0 + 26g + g2 = 0 + -45 26g + g2 = 0 + -45 Combine like terms: 0 + -45 = -45 26g + g2 = -45 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 = -45 + 169 Reorder the terms: 169 + 26g + g2 = -45 + 169 Combine like terms: -45 + 169 = 124 169 + 26g + g2 = 124 Factor a perfect square on the left side: (g + 13)(g + 13) = 124 Calculate the square root of the right side: 11.135528726 Break this problem into two subproblems by setting (g + 13) equal to 11.135528726 and -11.135528726.Subproblem 1
g + 13 = 11.135528726 Simplifying g + 13 = 11.135528726 Reorder the terms: 13 + g = 11.135528726 Solving 13 + g = 11.135528726 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 = 11.135528726 + -13 Combine like terms: 13 + -13 = 0 0 + g = 11.135528726 + -13 g = 11.135528726 + -13 Combine like terms: 11.135528726 + -13 = -1.864471274 g = -1.864471274 Simplifying g = -1.864471274Subproblem 2
g + 13 = -11.135528726 Simplifying g + 13 = -11.135528726 Reorder the terms: 13 + g = -11.135528726 Solving 13 + g = -11.135528726 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 = -11.135528726 + -13 Combine like terms: 13 + -13 = 0 0 + g = -11.135528726 + -13 g = -11.135528726 + -13 Combine like terms: -11.135528726 + -13 = -24.135528726 g = -24.135528726 Simplifying g = -24.135528726Solution
The solution to the problem is based on the solutions from the subproblems. g = {-1.864471274, -24.135528726}
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