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Simplifying 85x2 + -35x + -23 = 0 Reorder the terms: -23 + -35x + 85x2 = 0 Solving -23 + -35x + 85x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 85 the coefficient of the squared term: Divide each side by '85'. -0.2705882353 + -0.4117647059x + x2 = 0 Move the constant term to the right: Add '0.2705882353' to each side of the equation. -0.2705882353 + -0.4117647059x + 0.2705882353 + x2 = 0 + 0.2705882353 Reorder the terms: -0.2705882353 + 0.2705882353 + -0.4117647059x + x2 = 0 + 0.2705882353 Combine like terms: -0.2705882353 + 0.2705882353 = 0.0000000000 0.0000000000 + -0.4117647059x + x2 = 0 + 0.2705882353 -0.4117647059x + x2 = 0 + 0.2705882353 Combine like terms: 0 + 0.2705882353 = 0.2705882353 -0.4117647059x + x2 = 0.2705882353 The x term is -0.4117647059x. Take half its coefficient (-0.205882353). Square it (0.04238754328) and add it to both sides. Add '0.04238754328' to each side of the equation. -0.4117647059x + 0.04238754328 + x2 = 0.2705882353 + 0.04238754328 Reorder the terms: 0.04238754328 + -0.4117647059x + x2 = 0.2705882353 + 0.04238754328 Combine like terms: 0.2705882353 + 0.04238754328 = 0.31297577858 0.04238754328 + -0.4117647059x + x2 = 0.31297577858 Factor a perfect square on the left side: (x + -0.205882353)(x + -0.205882353) = 0.31297577858 Calculate the square root of the right side: 0.559442382 Break this problem into two subproblems by setting (x + -0.205882353) equal to 0.559442382 and -0.559442382.Subproblem 1
x + -0.205882353 = 0.559442382 Simplifying x + -0.205882353 = 0.559442382 Reorder the terms: -0.205882353 + x = 0.559442382 Solving -0.205882353 + x = 0.559442382 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.205882353' to each side of the equation. -0.205882353 + 0.205882353 + x = 0.559442382 + 0.205882353 Combine like terms: -0.205882353 + 0.205882353 = 0.000000000 0.000000000 + x = 0.559442382 + 0.205882353 x = 0.559442382 + 0.205882353 Combine like terms: 0.559442382 + 0.205882353 = 0.765324735 x = 0.765324735 Simplifying x = 0.765324735Subproblem 2
x + -0.205882353 = -0.559442382 Simplifying x + -0.205882353 = -0.559442382 Reorder the terms: -0.205882353 + x = -0.559442382 Solving -0.205882353 + x = -0.559442382 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.205882353' to each side of the equation. -0.205882353 + 0.205882353 + x = -0.559442382 + 0.205882353 Combine like terms: -0.205882353 + 0.205882353 = 0.000000000 0.000000000 + x = -0.559442382 + 0.205882353 x = -0.559442382 + 0.205882353 Combine like terms: -0.559442382 + 0.205882353 = -0.353560029 x = -0.353560029 Simplifying x = -0.353560029Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.765324735, -0.353560029}
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