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Simplifying -2g2 + -28g = -50 Reorder the terms: -28g + -2g2 = -50 Solving -28g + -2g2 = -50 Solving for variable 'g'. Reorder the terms: 50 + -28g + -2g2 = -50 + 50 Combine like terms: -50 + 50 = 0 50 + -28g + -2g2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(25 + -14g + -1g2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(25 + -14g + -1g2)' equal to zero and attempt to solve: Simplifying 25 + -14g + -1g2 = 0 Solving 25 + -14g + -1g2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -25 + 14g + g2 = 0 Move the constant term to the right: Add '25' to each side of the equation. -25 + 14g + 25 + g2 = 0 + 25 Reorder the terms: -25 + 25 + 14g + g2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 14g + g2 = 0 + 25 14g + g2 = 0 + 25 Combine like terms: 0 + 25 = 25 14g + g2 = 25 The g term is 14g. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14g + 49 + g2 = 25 + 49 Reorder the terms: 49 + 14g + g2 = 25 + 49 Combine like terms: 25 + 49 = 74 49 + 14g + g2 = 74 Factor a perfect square on the left side: (g + 7)(g + 7) = 74 Calculate the square root of the right side: 8.602325267 Break this problem into two subproblems by setting (g + 7) equal to 8.602325267 and -8.602325267.Subproblem 1
g + 7 = 8.602325267 Simplifying g + 7 = 8.602325267 Reorder the terms: 7 + g = 8.602325267 Solving 7 + g = 8.602325267 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + g = 8.602325267 + -7 Combine like terms: 7 + -7 = 0 0 + g = 8.602325267 + -7 g = 8.602325267 + -7 Combine like terms: 8.602325267 + -7 = 1.602325267 g = 1.602325267 Simplifying g = 1.602325267Subproblem 2
g + 7 = -8.602325267 Simplifying g + 7 = -8.602325267 Reorder the terms: 7 + g = -8.602325267 Solving 7 + g = -8.602325267 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + g = -8.602325267 + -7 Combine like terms: 7 + -7 = 0 0 + g = -8.602325267 + -7 g = -8.602325267 + -7 Combine like terms: -8.602325267 + -7 = -15.602325267 g = -15.602325267 Simplifying g = -15.602325267Solution
The solution to the problem is based on the solutions from the subproblems. g = {1.602325267, -15.602325267}Solution
g = {1.602325267, -15.602325267}
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