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Simplifying -1g2 + 4g + 3 = 0 Reorder the terms: 3 + 4g + -1g2 = 0 Solving 3 + 4g + -1g2 = 0 Solving for variable 'g'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -3 + -4g + g2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -4g + 3 + g2 = 0 + 3 Reorder the terms: -3 + 3 + -4g + g2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4g + g2 = 0 + 3 -4g + g2 = 0 + 3 Combine like terms: 0 + 3 = 3 -4g + g2 = 3 The g term is -4g. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4g + 4 + g2 = 3 + 4 Reorder the terms: 4 + -4g + g2 = 3 + 4 Combine like terms: 3 + 4 = 7 4 + -4g + g2 = 7 Factor a perfect square on the left side: (g + -2)(g + -2) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (g + -2) equal to 2.645751311 and -2.645751311.Subproblem 1
g + -2 = 2.645751311 Simplifying g + -2 = 2.645751311 Reorder the terms: -2 + g = 2.645751311 Solving -2 + g = 2.645751311 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + g = 2.645751311 + 2 Combine like terms: -2 + 2 = 0 0 + g = 2.645751311 + 2 g = 2.645751311 + 2 Combine like terms: 2.645751311 + 2 = 4.645751311 g = 4.645751311 Simplifying g = 4.645751311Subproblem 2
g + -2 = -2.645751311 Simplifying g + -2 = -2.645751311 Reorder the terms: -2 + g = -2.645751311 Solving -2 + g = -2.645751311 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + g = -2.645751311 + 2 Combine like terms: -2 + 2 = 0 0 + g = -2.645751311 + 2 g = -2.645751311 + 2 Combine like terms: -2.645751311 + 2 = -0.645751311 g = -0.645751311 Simplifying g = -0.645751311Solution
The solution to the problem is based on the solutions from the subproblems. g = {4.645751311, -0.645751311}
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