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Simplifying 10g2 + -10 = 29g Reorder the terms: -10 + 10g2 = 29g Solving -10 + 10g2 = 29g Solving for variable 'g'. Reorder the terms: -10 + -29g + 10g2 = 29g + -29g Combine like terms: 29g + -29g = 0 -10 + -29g + 10g2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -1 + -2.9g + g2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -2.9g + 1 + g2 = 0 + 1 Reorder the terms: -1 + 1 + -2.9g + g2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2.9g + g2 = 0 + 1 -2.9g + g2 = 0 + 1 Combine like terms: 0 + 1 = 1 -2.9g + g2 = 1 The g term is -2.9g. Take half its coefficient (-1.45). Square it (2.1025) and add it to both sides. Add '2.1025' to each side of the equation. -2.9g + 2.1025 + g2 = 1 + 2.1025 Reorder the terms: 2.1025 + -2.9g + g2 = 1 + 2.1025 Combine like terms: 1 + 2.1025 = 3.1025 2.1025 + -2.9g + g2 = 3.1025 Factor a perfect square on the left side: (g + -1.45)(g + -1.45) = 3.1025 Calculate the square root of the right side: 1.761391495 Break this problem into two subproblems by setting (g + -1.45) equal to 1.761391495 and -1.761391495.Subproblem 1
g + -1.45 = 1.761391495 Simplifying g + -1.45 = 1.761391495 Reorder the terms: -1.45 + g = 1.761391495 Solving -1.45 + g = 1.761391495 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '1.45' to each side of the equation. -1.45 + 1.45 + g = 1.761391495 + 1.45 Combine like terms: -1.45 + 1.45 = 0.00 0.00 + g = 1.761391495 + 1.45 g = 1.761391495 + 1.45 Combine like terms: 1.761391495 + 1.45 = 3.211391495 g = 3.211391495 Simplifying g = 3.211391495Subproblem 2
g + -1.45 = -1.761391495 Simplifying g + -1.45 = -1.761391495 Reorder the terms: -1.45 + g = -1.761391495 Solving -1.45 + g = -1.761391495 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '1.45' to each side of the equation. -1.45 + 1.45 + g = -1.761391495 + 1.45 Combine like terms: -1.45 + 1.45 = 0.00 0.00 + g = -1.761391495 + 1.45 g = -1.761391495 + 1.45 Combine like terms: -1.761391495 + 1.45 = -0.311391495 g = -0.311391495 Simplifying g = -0.311391495Solution
The solution to the problem is based on the solutions from the subproblems. g = {3.211391495, -0.311391495}
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