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Simplifying 4g2 + -7g + -4 = 0 Reorder the terms: -4 + -7g + 4g2 = 0 Solving -4 + -7g + 4g2 = 0 Solving for variable 'g'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1 + -1.75g + g2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -1.75g + 1 + g2 = 0 + 1 Reorder the terms: -1 + 1 + -1.75g + g2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1.75g + g2 = 0 + 1 -1.75g + g2 = 0 + 1 Combine like terms: 0 + 1 = 1 -1.75g + g2 = 1 The g term is -1.75g. Take half its coefficient (-0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. -1.75g + 0.765625 + g2 = 1 + 0.765625 Reorder the terms: 0.765625 + -1.75g + g2 = 1 + 0.765625 Combine like terms: 1 + 0.765625 = 1.765625 0.765625 + -1.75g + g2 = 1.765625 Factor a perfect square on the left side: (g + -0.875)(g + -0.875) = 1.765625 Calculate the square root of the right side: 1.328768227 Break this problem into two subproblems by setting (g + -0.875) equal to 1.328768227 and -1.328768227.Subproblem 1
g + -0.875 = 1.328768227 Simplifying g + -0.875 = 1.328768227 Reorder the terms: -0.875 + g = 1.328768227 Solving -0.875 + g = 1.328768227 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + g = 1.328768227 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + g = 1.328768227 + 0.875 g = 1.328768227 + 0.875 Combine like terms: 1.328768227 + 0.875 = 2.203768227 g = 2.203768227 Simplifying g = 2.203768227Subproblem 2
g + -0.875 = -1.328768227 Simplifying g + -0.875 = -1.328768227 Reorder the terms: -0.875 + g = -1.328768227 Solving -0.875 + g = -1.328768227 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + g = -1.328768227 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + g = -1.328768227 + 0.875 g = -1.328768227 + 0.875 Combine like terms: -1.328768227 + 0.875 = -0.453768227 g = -0.453768227 Simplifying g = -0.453768227Solution
The solution to the problem is based on the solutions from the subproblems. g = {2.203768227, -0.453768227}
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