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Simplifying g2 + -10g + 15 = 0 Reorder the terms: 15 + -10g + g2 = 0 Solving 15 + -10g + g2 = 0 Solving for variable 'g'. Begin completing the square. Move the constant term to the right: Add '-15' to each side of the equation. 15 + -10g + -15 + g2 = 0 + -15 Reorder the terms: 15 + -15 + -10g + g2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -10g + g2 = 0 + -15 -10g + g2 = 0 + -15 Combine like terms: 0 + -15 = -15 -10g + g2 = -15 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 = -15 + 25 Reorder the terms: 25 + -10g + g2 = -15 + 25 Combine like terms: -15 + 25 = 10 25 + -10g + g2 = 10 Factor a perfect square on the left side: (g + -5)(g + -5) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (g + -5) equal to 3.16227766 and -3.16227766.Subproblem 1
g + -5 = 3.16227766 Simplifying g + -5 = 3.16227766 Reorder the terms: -5 + g = 3.16227766 Solving -5 + g = 3.16227766 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 = 3.16227766 + 5 Combine like terms: -5 + 5 = 0 0 + g = 3.16227766 + 5 g = 3.16227766 + 5 Combine like terms: 3.16227766 + 5 = 8.16227766 g = 8.16227766 Simplifying g = 8.16227766Subproblem 2
g + -5 = -3.16227766 Simplifying g + -5 = -3.16227766 Reorder the terms: -5 + g = -3.16227766 Solving -5 + g = -3.16227766 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 = -3.16227766 + 5 Combine like terms: -5 + 5 = 0 0 + g = -3.16227766 + 5 g = -3.16227766 + 5 Combine like terms: -3.16227766 + 5 = 1.83772234 g = 1.83772234 Simplifying g = 1.83772234Solution
The solution to the problem is based on the solutions from the subproblems. g = {8.16227766, 1.83772234}
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