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Simplifying -0.8g2 + 14.4g + 2 = 0 Reorder the terms: 2 + 14.4g + -0.8g2 = 0 Solving 2 + 14.4g + -0.8g2 = 0 Solving for variable 'g'. Begin completing the square. Divide all terms by -0.8 the coefficient of the squared term: Divide each side by '-0.8'. -2.5 + -18g + g2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -18g + 2.5 + g2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -18g + g2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -18g + g2 = 0 + 2.5 -18g + g2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -18g + g2 = 2.5 The g term is -18g. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18g + 81 + g2 = 2.5 + 81 Reorder the terms: 81 + -18g + g2 = 2.5 + 81 Combine like terms: 2.5 + 81 = 83.5 81 + -18g + g2 = 83.5 Factor a perfect square on the left side: (g + -9)(g + -9) = 83.5 Calculate the square root of the right side: 9.137833441 Break this problem into two subproblems by setting (g + -9) equal to 9.137833441 and -9.137833441.Subproblem 1
g + -9 = 9.137833441 Simplifying g + -9 = 9.137833441 Reorder the terms: -9 + g = 9.137833441 Solving -9 + g = 9.137833441 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + g = 9.137833441 + 9 Combine like terms: -9 + 9 = 0 0 + g = 9.137833441 + 9 g = 9.137833441 + 9 Combine like terms: 9.137833441 + 9 = 18.137833441 g = 18.137833441 Simplifying g = 18.137833441Subproblem 2
g + -9 = -9.137833441 Simplifying g + -9 = -9.137833441 Reorder the terms: -9 + g = -9.137833441 Solving -9 + g = -9.137833441 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + g = -9.137833441 + 9 Combine like terms: -9 + 9 = 0 0 + g = -9.137833441 + 9 g = -9.137833441 + 9 Combine like terms: -9.137833441 + 9 = -0.137833441 g = -0.137833441 Simplifying g = -0.137833441Solution
The solution to the problem is based on the solutions from the subproblems. g = {18.137833441, -0.137833441}
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