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Simplifying g2 + -22g + -25 = 0 Reorder the terms: -25 + -22g + g2 = 0 Solving -25 + -22g + g2 = 0 Solving for variable 'g'. Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + -22g + 25 + g2 = 0 + 25 Reorder the terms: -25 + 25 + -22g + g2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -22g + g2 = 0 + 25 -22g + g2 = 0 + 25 Combine like terms: 0 + 25 = 25 -22g + g2 = 25 The g term is -22g. Take half its coefficient (-11). Square it (121) and add it to both sides. Add '121' to each side of the equation. -22g + 121 + g2 = 25 + 121 Reorder the terms: 121 + -22g + g2 = 25 + 121 Combine like terms: 25 + 121 = 146 121 + -22g + g2 = 146 Factor a perfect square on the left side: (g + -11)(g + -11) = 146 Calculate the square root of the right side: 12.083045974 Break this problem into two subproblems by setting (g + -11) equal to 12.083045974 and -12.083045974.Subproblem 1
g + -11 = 12.083045974 Simplifying g + -11 = 12.083045974 Reorder the terms: -11 + g = 12.083045974 Solving -11 + g = 12.083045974 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + g = 12.083045974 + 11 Combine like terms: -11 + 11 = 0 0 + g = 12.083045974 + 11 g = 12.083045974 + 11 Combine like terms: 12.083045974 + 11 = 23.083045974 g = 23.083045974 Simplifying g = 23.083045974Subproblem 2
g + -11 = -12.083045974 Simplifying g + -11 = -12.083045974 Reorder the terms: -11 + g = -12.083045974 Solving -11 + g = -12.083045974 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + g = -12.083045974 + 11 Combine like terms: -11 + 11 = 0 0 + g = -12.083045974 + 11 g = -12.083045974 + 11 Combine like terms: -12.083045974 + 11 = -1.083045974 g = -1.083045974 Simplifying g = -1.083045974Solution
The solution to the problem is based on the solutions from the subproblems. g = {23.083045974, -1.083045974}
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