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Simplifying 29g2 + -76g + -16 = 0 Reorder the terms: -16 + -76g + 29g2 = 0 Solving -16 + -76g + 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'. -0.5517241379 + -2.620689655g + g2 = 0 Move the constant term to the right: Add '0.5517241379' to each side of the equation. -0.5517241379 + -2.620689655g + 0.5517241379 + g2 = 0 + 0.5517241379 Reorder the terms: -0.5517241379 + 0.5517241379 + -2.620689655g + g2 = 0 + 0.5517241379 Combine like terms: -0.5517241379 + 0.5517241379 = 0.0000000000 0.0000000000 + -2.620689655g + g2 = 0 + 0.5517241379 -2.620689655g + g2 = 0 + 0.5517241379 Combine like terms: 0 + 0.5517241379 = 0.5517241379 -2.620689655g + g2 = 0.5517241379 The g term is -2.620689655g. Take half its coefficient (-1.310344828). Square it (1.717003568) and add it to both sides. Add '1.717003568' to each side of the equation. -2.620689655g + 1.717003568 + g2 = 0.5517241379 + 1.717003568 Reorder the terms: 1.717003568 + -2.620689655g + g2 = 0.5517241379 + 1.717003568 Combine like terms: 0.5517241379 + 1.717003568 = 2.2687277059 1.717003568 + -2.620689655g + g2 = 2.2687277059 Factor a perfect square on the left side: (g + -1.310344828)(g + -1.310344828) = 2.2687277059 Calculate the square root of the right side: 1.506229633 Break this problem into two subproblems by setting (g + -1.310344828) equal to 1.506229633 and -1.506229633.Subproblem 1
g + -1.310344828 = 1.506229633 Simplifying g + -1.310344828 = 1.506229633 Reorder the terms: -1.310344828 + g = 1.506229633 Solving -1.310344828 + g = 1.506229633 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '1.310344828' to each side of the equation. -1.310344828 + 1.310344828 + g = 1.506229633 + 1.310344828 Combine like terms: -1.310344828 + 1.310344828 = 0.000000000 0.000000000 + g = 1.506229633 + 1.310344828 g = 1.506229633 + 1.310344828 Combine like terms: 1.506229633 + 1.310344828 = 2.816574461 g = 2.816574461 Simplifying g = 2.816574461Subproblem 2
g + -1.310344828 = -1.506229633 Simplifying g + -1.310344828 = -1.506229633 Reorder the terms: -1.310344828 + g = -1.506229633 Solving -1.310344828 + g = -1.506229633 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '1.310344828' to each side of the equation. -1.310344828 + 1.310344828 + g = -1.506229633 + 1.310344828 Combine like terms: -1.310344828 + 1.310344828 = 0.000000000 0.000000000 + g = -1.506229633 + 1.310344828 g = -1.506229633 + 1.310344828 Combine like terms: -1.506229633 + 1.310344828 = -0.195884805 g = -0.195884805 Simplifying g = -0.195884805Solution
The solution to the problem is based on the solutions from the subproblems. g = {2.816574461, -0.195884805}
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