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Simplifying g2 + -16g + 34 = 0 Reorder the terms: 34 + -16g + g2 = 0 Solving 34 + -16g + g2 = 0 Solving for variable 'g'. Begin completing the square. Move the constant term to the right: Add '-34' to each side of the equation. 34 + -16g + -34 + g2 = 0 + -34 Reorder the terms: 34 + -34 + -16g + g2 = 0 + -34 Combine like terms: 34 + -34 = 0 0 + -16g + g2 = 0 + -34 -16g + g2 = 0 + -34 Combine like terms: 0 + -34 = -34 -16g + g2 = -34 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 = -34 + 64 Reorder the terms: 64 + -16g + g2 = -34 + 64 Combine like terms: -34 + 64 = 30 64 + -16g + g2 = 30 Factor a perfect square on the left side: (g + -8)(g + -8) = 30 Calculate the square root of the right side: 5.477225575 Break this problem into two subproblems by setting (g + -8) equal to 5.477225575 and -5.477225575.Subproblem 1
g + -8 = 5.477225575 Simplifying g + -8 = 5.477225575 Reorder the terms: -8 + g = 5.477225575 Solving -8 + g = 5.477225575 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 = 5.477225575 + 8 Combine like terms: -8 + 8 = 0 0 + g = 5.477225575 + 8 g = 5.477225575 + 8 Combine like terms: 5.477225575 + 8 = 13.477225575 g = 13.477225575 Simplifying g = 13.477225575Subproblem 2
g + -8 = -5.477225575 Simplifying g + -8 = -5.477225575 Reorder the terms: -8 + g = -5.477225575 Solving -8 + g = -5.477225575 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 = -5.477225575 + 8 Combine like terms: -8 + 8 = 0 0 + g = -5.477225575 + 8 g = -5.477225575 + 8 Combine like terms: -5.477225575 + 8 = 2.522774425 g = 2.522774425 Simplifying g = 2.522774425Solution
The solution to the problem is based on the solutions from the subproblems. g = {13.477225575, 2.522774425}
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