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Simplifying g2 + -10g + 19 = 0 Reorder the terms: 19 + -10g + g2 = 0 Solving 19 + -10g + g2 = 0 Solving for variable 'g'. Begin completing the square. Move the constant term to the right: Add '-19' to each side of the equation. 19 + -10g + -19 + g2 = 0 + -19 Reorder the terms: 19 + -19 + -10g + g2 = 0 + -19 Combine like terms: 19 + -19 = 0 0 + -10g + g2 = 0 + -19 -10g + g2 = 0 + -19 Combine like terms: 0 + -19 = -19 -10g + g2 = -19 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 = -19 + 25 Reorder the terms: 25 + -10g + g2 = -19 + 25 Combine like terms: -19 + 25 = 6 25 + -10g + g2 = 6 Factor a perfect square on the left side: (g + -5)(g + -5) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (g + -5) equal to 2.449489743 and -2.449489743.Subproblem 1
g + -5 = 2.449489743 Simplifying g + -5 = 2.449489743 Reorder the terms: -5 + g = 2.449489743 Solving -5 + g = 2.449489743 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 = 2.449489743 + 5 Combine like terms: -5 + 5 = 0 0 + g = 2.449489743 + 5 g = 2.449489743 + 5 Combine like terms: 2.449489743 + 5 = 7.449489743 g = 7.449489743 Simplifying g = 7.449489743Subproblem 2
g + -5 = -2.449489743 Simplifying g + -5 = -2.449489743 Reorder the terms: -5 + g = -2.449489743 Solving -5 + g = -2.449489743 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 = -2.449489743 + 5 Combine like terms: -5 + 5 = 0 0 + g = -2.449489743 + 5 g = -2.449489743 + 5 Combine like terms: -2.449489743 + 5 = 2.550510257 g = 2.550510257 Simplifying g = 2.550510257Solution
The solution to the problem is based on the solutions from the subproblems. g = {7.449489743, 2.550510257}
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