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Simplifying g2 + 16g + 45 = 0 Reorder the terms: 45 + 16g + g2 = 0 Solving 45 + 16g + 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 + 16g + -45 + g2 = 0 + -45 Reorder the terms: 45 + -45 + 16g + g2 = 0 + -45 Combine like terms: 45 + -45 = 0 0 + 16g + g2 = 0 + -45 16g + g2 = 0 + -45 Combine like terms: 0 + -45 = -45 16g + g2 = -45 The g term is 16g. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16g + 64 + g2 = -45 + 64 Reorder the terms: 64 + 16g + g2 = -45 + 64 Combine like terms: -45 + 64 = 19 64 + 16g + g2 = 19 Factor a perfect square on the left side: (g + 8)(g + 8) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (g + 8) equal to 4.358898944 and -4.358898944.Subproblem 1
g + 8 = 4.358898944 Simplifying g + 8 = 4.358898944 Reorder the terms: 8 + g = 4.358898944 Solving 8 + g = 4.358898944 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + g = 4.358898944 + -8 Combine like terms: 8 + -8 = 0 0 + g = 4.358898944 + -8 g = 4.358898944 + -8 Combine like terms: 4.358898944 + -8 = -3.641101056 g = -3.641101056 Simplifying g = -3.641101056Subproblem 2
g + 8 = -4.358898944 Simplifying g + 8 = -4.358898944 Reorder the terms: 8 + g = -4.358898944 Solving 8 + g = -4.358898944 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + g = -4.358898944 + -8 Combine like terms: 8 + -8 = 0 0 + g = -4.358898944 + -8 g = -4.358898944 + -8 Combine like terms: -4.358898944 + -8 = -12.358898944 g = -12.358898944 Simplifying g = -12.358898944Solution
The solution to the problem is based on the solutions from the subproblems. g = {-3.641101056, -12.358898944}
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