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Simplifying 38x2 + -86x + 32 = 0 Reorder the terms: 32 + -86x + 38x2 = 0 Solving 32 + -86x + 38x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(16 + -43x + 19x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(16 + -43x + 19x2)' equal to zero and attempt to solve: Simplifying 16 + -43x + 19x2 = 0 Solving 16 + -43x + 19x2 = 0 Begin completing the square. Divide all terms by 19 the coefficient of the squared term: Divide each side by '19'. 0.8421052632 + -2.263157895x + x2 = 0 Move the constant term to the right: Add '-0.8421052632' to each side of the equation. 0.8421052632 + -2.263157895x + -0.8421052632 + x2 = 0 + -0.8421052632 Reorder the terms: 0.8421052632 + -0.8421052632 + -2.263157895x + x2 = 0 + -0.8421052632 Combine like terms: 0.8421052632 + -0.8421052632 = 0.0000000000 0.0000000000 + -2.263157895x + x2 = 0 + -0.8421052632 -2.263157895x + x2 = 0 + -0.8421052632 Combine like terms: 0 + -0.8421052632 = -0.8421052632 -2.263157895x + x2 = -0.8421052632 The x term is -2.263157895x. Take half its coefficient (-1.131578948). Square it (1.280470916) and add it to both sides. Add '1.280470916' to each side of the equation. -2.263157895x + 1.280470916 + x2 = -0.8421052632 + 1.280470916 Reorder the terms: 1.280470916 + -2.263157895x + x2 = -0.8421052632 + 1.280470916 Combine like terms: -0.8421052632 + 1.280470916 = 0.4383656528 1.280470916 + -2.263157895x + x2 = 0.4383656528 Factor a perfect square on the left side: (x + -1.131578948)(x + -1.131578948) = 0.4383656528 Calculate the square root of the right side: 0.662091876 Break this problem into two subproblems by setting (x + -1.131578948) equal to 0.662091876 and -0.662091876.Subproblem 1
x + -1.131578948 = 0.662091876 Simplifying x + -1.131578948 = 0.662091876 Reorder the terms: -1.131578948 + x = 0.662091876 Solving -1.131578948 + x = 0.662091876 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.131578948' to each side of the equation. -1.131578948 + 1.131578948 + x = 0.662091876 + 1.131578948 Combine like terms: -1.131578948 + 1.131578948 = 0.000000000 0.000000000 + x = 0.662091876 + 1.131578948 x = 0.662091876 + 1.131578948 Combine like terms: 0.662091876 + 1.131578948 = 1.793670824 x = 1.793670824 Simplifying x = 1.793670824Subproblem 2
x + -1.131578948 = -0.662091876 Simplifying x + -1.131578948 = -0.662091876 Reorder the terms: -1.131578948 + x = -0.662091876 Solving -1.131578948 + x = -0.662091876 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.131578948' to each side of the equation. -1.131578948 + 1.131578948 + x = -0.662091876 + 1.131578948 Combine like terms: -1.131578948 + 1.131578948 = 0.000000000 0.000000000 + x = -0.662091876 + 1.131578948 x = -0.662091876 + 1.131578948 Combine like terms: -0.662091876 + 1.131578948 = 0.469487072 x = 0.469487072 Simplifying x = 0.469487072Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.793670824, 0.469487072}Solution
x = {1.793670824, 0.469487072}
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