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Simplifying 29g2 + -18g + -15 = 0 Reorder the terms: -15 + -18g + 29g2 = 0 Solving -15 + -18g + 29g2 = 0 Solving for variable 'g'. Begin completing the square. Divide all terms by 29 the coefficient of the squared term: Divide each side by '29'. -0.5172413793 + -0.6206896552g + g2 = 0 Move the constant term to the right: Add '0.5172413793' to each side of the equation. -0.5172413793 + -0.6206896552g + 0.5172413793 + g2 = 0 + 0.5172413793 Reorder the terms: -0.5172413793 + 0.5172413793 + -0.6206896552g + g2 = 0 + 0.5172413793 Combine like terms: -0.5172413793 + 0.5172413793 = 0.0000000000 0.0000000000 + -0.6206896552g + g2 = 0 + 0.5172413793 -0.6206896552g + g2 = 0 + 0.5172413793 Combine like terms: 0 + 0.5172413793 = 0.5172413793 -0.6206896552g + g2 = 0.5172413793 The g term is -0.6206896552g. Take half its coefficient (-0.3103448276). Square it (0.09631391202) and add it to both sides. Add '0.09631391202' to each side of the equation. -0.6206896552g + 0.09631391202 + g2 = 0.5172413793 + 0.09631391202 Reorder the terms: 0.09631391202 + -0.6206896552g + g2 = 0.5172413793 + 0.09631391202 Combine like terms: 0.5172413793 + 0.09631391202 = 0.61355529132 0.09631391202 + -0.6206896552g + g2 = 0.61355529132 Factor a perfect square on the left side: (g + -0.3103448276)(g + -0.3103448276) = 0.61355529132 Calculate the square root of the right side: 0.783297703 Break this problem into two subproblems by setting (g + -0.3103448276) equal to 0.783297703 and -0.783297703.Subproblem 1
g + -0.3103448276 = 0.783297703 Simplifying g + -0.3103448276 = 0.783297703 Reorder the terms: -0.3103448276 + g = 0.783297703 Solving -0.3103448276 + g = 0.783297703 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '0.3103448276' to each side of the equation. -0.3103448276 + 0.3103448276 + g = 0.783297703 + 0.3103448276 Combine like terms: -0.3103448276 + 0.3103448276 = 0.0000000000 0.0000000000 + g = 0.783297703 + 0.3103448276 g = 0.783297703 + 0.3103448276 Combine like terms: 0.783297703 + 0.3103448276 = 1.0936425306 g = 1.0936425306 Simplifying g = 1.0936425306Subproblem 2
g + -0.3103448276 = -0.783297703 Simplifying g + -0.3103448276 = -0.783297703 Reorder the terms: -0.3103448276 + g = -0.783297703 Solving -0.3103448276 + g = -0.783297703 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '0.3103448276' to each side of the equation. -0.3103448276 + 0.3103448276 + g = -0.783297703 + 0.3103448276 Combine like terms: -0.3103448276 + 0.3103448276 = 0.0000000000 0.0000000000 + g = -0.783297703 + 0.3103448276 g = -0.783297703 + 0.3103448276 Combine like terms: -0.783297703 + 0.3103448276 = -0.4729528754 g = -0.4729528754 Simplifying g = -0.4729528754Solution
The solution to the problem is based on the solutions from the subproblems. g = {1.0936425306, -0.4729528754}
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