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Simplifying g2 + -10g + 8 = 0 Reorder the terms: 8 + -10g + g2 = 0 Solving 8 + -10g + g2 = 0 Solving for variable 'g'. Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + -10g + -8 + g2 = 0 + -8 Reorder the terms: 8 + -8 + -10g + g2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -10g + g2 = 0 + -8 -10g + g2 = 0 + -8 Combine like terms: 0 + -8 = -8 -10g + g2 = -8 The g term is -10g. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10g + 25 + g2 = -8 + 25 Reorder the terms: 25 + -10g + g2 = -8 + 25 Combine like terms: -8 + 25 = 17 25 + -10g + g2 = 17 Factor a perfect square on the left side: (g + -5)(g + -5) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (g + -5) equal to 4.123105626 and -4.123105626.Subproblem 1
g + -5 = 4.123105626 Simplifying g + -5 = 4.123105626 Reorder the terms: -5 + g = 4.123105626 Solving -5 + g = 4.123105626 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + g = 4.123105626 + 5 Combine like terms: -5 + 5 = 0 0 + g = 4.123105626 + 5 g = 4.123105626 + 5 Combine like terms: 4.123105626 + 5 = 9.123105626 g = 9.123105626 Simplifying g = 9.123105626Subproblem 2
g + -5 = -4.123105626 Simplifying g + -5 = -4.123105626 Reorder the terms: -5 + g = -4.123105626 Solving -5 + g = -4.123105626 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + g = -4.123105626 + 5 Combine like terms: -5 + 5 = 0 0 + g = -4.123105626 + 5 g = -4.123105626 + 5 Combine like terms: -4.123105626 + 5 = 0.876894374 g = 0.876894374 Simplifying g = 0.876894374Solution
The solution to the problem is based on the solutions from the subproblems. g = {9.123105626, 0.876894374}
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