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Simplifying -4g2 + 9g + 7 = 0 Reorder the terms: 7 + 9g + -4g2 = 0 Solving 7 + 9g + -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'. -1.75 + -2.25g + g2 = 0 Move the constant term to the right: Add '1.75' to each side of the equation. -1.75 + -2.25g + 1.75 + g2 = 0 + 1.75 Reorder the terms: -1.75 + 1.75 + -2.25g + g2 = 0 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + -2.25g + g2 = 0 + 1.75 -2.25g + g2 = 0 + 1.75 Combine like terms: 0 + 1.75 = 1.75 -2.25g + g2 = 1.75 The g term is -2.25g. Take half its coefficient (-1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. -2.25g + 1.265625 + g2 = 1.75 + 1.265625 Reorder the terms: 1.265625 + -2.25g + g2 = 1.75 + 1.265625 Combine like terms: 1.75 + 1.265625 = 3.015625 1.265625 + -2.25g + g2 = 3.015625 Factor a perfect square on the left side: (g + -1.125)(g + -1.125) = 3.015625 Calculate the square root of the right side: 1.736555499 Break this problem into two subproblems by setting (g + -1.125) equal to 1.736555499 and -1.736555499.Subproblem 1
g + -1.125 = 1.736555499 Simplifying g + -1.125 = 1.736555499 Reorder the terms: -1.125 + g = 1.736555499 Solving -1.125 + g = 1.736555499 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + g = 1.736555499 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + g = 1.736555499 + 1.125 g = 1.736555499 + 1.125 Combine like terms: 1.736555499 + 1.125 = 2.861555499 g = 2.861555499 Simplifying g = 2.861555499Subproblem 2
g + -1.125 = -1.736555499 Simplifying g + -1.125 = -1.736555499 Reorder the terms: -1.125 + g = -1.736555499 Solving -1.125 + g = -1.736555499 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + g = -1.736555499 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + g = -1.736555499 + 1.125 g = -1.736555499 + 1.125 Combine like terms: -1.736555499 + 1.125 = -0.611555499 g = -0.611555499 Simplifying g = -0.611555499Solution
The solution to the problem is based on the solutions from the subproblems. g = {2.861555499, -0.611555499}
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