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Simplifying g2 + -55g + 150 = 0 Reorder the terms: 150 + -55g + g2 = 0 Solving 150 + -55g + g2 = 0 Solving for variable 'g'. Begin completing the square. Move the constant term to the right: Add '-150' to each side of the equation. 150 + -55g + -150 + g2 = 0 + -150 Reorder the terms: 150 + -150 + -55g + g2 = 0 + -150 Combine like terms: 150 + -150 = 0 0 + -55g + g2 = 0 + -150 -55g + g2 = 0 + -150 Combine like terms: 0 + -150 = -150 -55g + g2 = -150 The g term is -55g. Take half its coefficient (-27.5). Square it (756.25) and add it to both sides. Add '756.25' to each side of the equation. -55g + 756.25 + g2 = -150 + 756.25 Reorder the terms: 756.25 + -55g + g2 = -150 + 756.25 Combine like terms: -150 + 756.25 = 606.25 756.25 + -55g + g2 = 606.25 Factor a perfect square on the left side: (g + -27.5)(g + -27.5) = 606.25 Calculate the square root of the right side: 24.622144504 Break this problem into two subproblems by setting (g + -27.5) equal to 24.622144504 and -24.622144504.Subproblem 1
g + -27.5 = 24.622144504 Simplifying g + -27.5 = 24.622144504 Reorder the terms: -27.5 + g = 24.622144504 Solving -27.5 + g = 24.622144504 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '27.5' to each side of the equation. -27.5 + 27.5 + g = 24.622144504 + 27.5 Combine like terms: -27.5 + 27.5 = 0.0 0.0 + g = 24.622144504 + 27.5 g = 24.622144504 + 27.5 Combine like terms: 24.622144504 + 27.5 = 52.122144504 g = 52.122144504 Simplifying g = 52.122144504Subproblem 2
g + -27.5 = -24.622144504 Simplifying g + -27.5 = -24.622144504 Reorder the terms: -27.5 + g = -24.622144504 Solving -27.5 + g = -24.622144504 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '27.5' to each side of the equation. -27.5 + 27.5 + g = -24.622144504 + 27.5 Combine like terms: -27.5 + 27.5 = 0.0 0.0 + g = -24.622144504 + 27.5 g = -24.622144504 + 27.5 Combine like terms: -24.622144504 + 27.5 = 2.877855496 g = 2.877855496 Simplifying g = 2.877855496Solution
The solution to the problem is based on the solutions from the subproblems. g = {52.122144504, 2.877855496}
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