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Simplifying 5g2 + -21 = 10g Reorder the terms: -21 + 5g2 = 10g Solving -21 + 5g2 = 10g Solving for variable 'g'. Reorder the terms: -21 + -10g + 5g2 = 10g + -10g Combine like terms: 10g + -10g = 0 -21 + -10g + 5g2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -4.2 + -2g + g2 = 0 Move the constant term to the right: Add '4.2' to each side of the equation. -4.2 + -2g + 4.2 + g2 = 0 + 4.2 Reorder the terms: -4.2 + 4.2 + -2g + g2 = 0 + 4.2 Combine like terms: -4.2 + 4.2 = 0.0 0.0 + -2g + g2 = 0 + 4.2 -2g + g2 = 0 + 4.2 Combine like terms: 0 + 4.2 = 4.2 -2g + g2 = 4.2 The g term is -2g. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2g + 1 + g2 = 4.2 + 1 Reorder the terms: 1 + -2g + g2 = 4.2 + 1 Combine like terms: 4.2 + 1 = 5.2 1 + -2g + g2 = 5.2 Factor a perfect square on the left side: (g + -1)(g + -1) = 5.2 Calculate the square root of the right side: 2.28035085 Break this problem into two subproblems by setting (g + -1) equal to 2.28035085 and -2.28035085.Subproblem 1
g + -1 = 2.28035085 Simplifying g + -1 = 2.28035085 Reorder the terms: -1 + g = 2.28035085 Solving -1 + g = 2.28035085 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + g = 2.28035085 + 1 Combine like terms: -1 + 1 = 0 0 + g = 2.28035085 + 1 g = 2.28035085 + 1 Combine like terms: 2.28035085 + 1 = 3.28035085 g = 3.28035085 Simplifying g = 3.28035085Subproblem 2
g + -1 = -2.28035085 Simplifying g + -1 = -2.28035085 Reorder the terms: -1 + g = -2.28035085 Solving -1 + g = -2.28035085 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + g = -2.28035085 + 1 Combine like terms: -1 + 1 = 0 0 + g = -2.28035085 + 1 g = -2.28035085 + 1 Combine like terms: -2.28035085 + 1 = -1.28035085 g = -1.28035085 Simplifying g = -1.28035085Solution
The solution to the problem is based on the solutions from the subproblems. g = {3.28035085, -1.28035085}
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