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Simplifying 3g + -4g + 2 + -7g2 + 5g + -1 = 0 Reorder the terms: 2 + -1 + 3g + -4g + 5g + -7g2 = 0 Combine like terms: 2 + -1 = 1 1 + 3g + -4g + 5g + -7g2 = 0 Combine like terms: 3g + -4g = -1g 1 + -1g + 5g + -7g2 = 0 Combine like terms: -1g + 5g = 4g 1 + 4g + -7g2 = 0 Solving 1 + 4g + -7g2 = 0 Solving for variable 'g'. Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -0.1428571429 + -0.5714285714g + g2 = 0 Move the constant term to the right: Add '0.1428571429' to each side of the equation. -0.1428571429 + -0.5714285714g + 0.1428571429 + g2 = 0 + 0.1428571429 Reorder the terms: -0.1428571429 + 0.1428571429 + -0.5714285714g + g2 = 0 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + -0.5714285714g + g2 = 0 + 0.1428571429 -0.5714285714g + g2 = 0 + 0.1428571429 Combine like terms: 0 + 0.1428571429 = 0.1428571429 -0.5714285714g + g2 = 0.1428571429 The g term is -0.5714285714g. Take half its coefficient (-0.2857142857). Square it (0.08163265305) and add it to both sides. Add '0.08163265305' to each side of the equation. -0.5714285714g + 0.08163265305 + g2 = 0.1428571429 + 0.08163265305 Reorder the terms: 0.08163265305 + -0.5714285714g + g2 = 0.1428571429 + 0.08163265305 Combine like terms: 0.1428571429 + 0.08163265305 = 0.22448979595 0.08163265305 + -0.5714285714g + g2 = 0.22448979595 Factor a perfect square on the left side: (g + -0.2857142857)(g + -0.2857142857) = 0.22448979595 Calculate the square root of the right side: 0.473803542 Break this problem into two subproblems by setting (g + -0.2857142857) equal to 0.473803542 and -0.473803542.Subproblem 1
g + -0.2857142857 = 0.473803542 Simplifying g + -0.2857142857 = 0.473803542 Reorder the terms: -0.2857142857 + g = 0.473803542 Solving -0.2857142857 + g = 0.473803542 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.2857142857 + g = 0.473803542 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + g = 0.473803542 + 0.2857142857 g = 0.473803542 + 0.2857142857 Combine like terms: 0.473803542 + 0.2857142857 = 0.7595178277 g = 0.7595178277 Simplifying g = 0.7595178277Subproblem 2
g + -0.2857142857 = -0.473803542 Simplifying g + -0.2857142857 = -0.473803542 Reorder the terms: -0.2857142857 + g = -0.473803542 Solving -0.2857142857 + g = -0.473803542 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.2857142857 + g = -0.473803542 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + g = -0.473803542 + 0.2857142857 g = -0.473803542 + 0.2857142857 Combine like terms: -0.473803542 + 0.2857142857 = -0.1880892563 g = -0.1880892563 Simplifying g = -0.1880892563Solution
The solution to the problem is based on the solutions from the subproblems. g = {0.7595178277, -0.1880892563}
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