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Simplifying 49x2 + -39x + 2 = 0 Reorder the terms: 2 + -39x + 49x2 = 0 Solving 2 + -39x + 49x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. 0.04081632653 + -0.7959183673x + x2 = 0 Move the constant term to the right: Add '-0.04081632653' to each side of the equation. 0.04081632653 + -0.7959183673x + -0.04081632653 + x2 = 0 + -0.04081632653 Reorder the terms: 0.04081632653 + -0.04081632653 + -0.7959183673x + x2 = 0 + -0.04081632653 Combine like terms: 0.04081632653 + -0.04081632653 = 0.00000000000 0.00000000000 + -0.7959183673x + x2 = 0 + -0.04081632653 -0.7959183673x + x2 = 0 + -0.04081632653 Combine like terms: 0 + -0.04081632653 = -0.04081632653 -0.7959183673x + x2 = -0.04081632653 The x term is -0.7959183673x. Take half its coefficient (-0.3979591837). Square it (0.1583715119) and add it to both sides. Add '0.1583715119' to each side of the equation. -0.7959183673x + 0.1583715119 + x2 = -0.04081632653 + 0.1583715119 Reorder the terms: 0.1583715119 + -0.7959183673x + x2 = -0.04081632653 + 0.1583715119 Combine like terms: -0.04081632653 + 0.1583715119 = 0.11755518537 0.1583715119 + -0.7959183673x + x2 = 0.11755518537 Factor a perfect square on the left side: (x + -0.3979591837)(x + -0.3979591837) = 0.11755518537 Calculate the square root of the right side: 0.342863217 Break this problem into two subproblems by setting (x + -0.3979591837) equal to 0.342863217 and -0.342863217.Subproblem 1
x + -0.3979591837 = 0.342863217 Simplifying x + -0.3979591837 = 0.342863217 Reorder the terms: -0.3979591837 + x = 0.342863217 Solving -0.3979591837 + x = 0.342863217 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3979591837' to each side of the equation. -0.3979591837 + 0.3979591837 + x = 0.342863217 + 0.3979591837 Combine like terms: -0.3979591837 + 0.3979591837 = 0.0000000000 0.0000000000 + x = 0.342863217 + 0.3979591837 x = 0.342863217 + 0.3979591837 Combine like terms: 0.342863217 + 0.3979591837 = 0.7408224007 x = 0.7408224007 Simplifying x = 0.7408224007Subproblem 2
x + -0.3979591837 = -0.342863217 Simplifying x + -0.3979591837 = -0.342863217 Reorder the terms: -0.3979591837 + x = -0.342863217 Solving -0.3979591837 + x = -0.342863217 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3979591837' to each side of the equation. -0.3979591837 + 0.3979591837 + x = -0.342863217 + 0.3979591837 Combine like terms: -0.3979591837 + 0.3979591837 = 0.0000000000 0.0000000000 + x = -0.342863217 + 0.3979591837 x = -0.342863217 + 0.3979591837 Combine like terms: -0.342863217 + 0.3979591837 = 0.0550959667 x = 0.0550959667 Simplifying x = 0.0550959667Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7408224007, 0.0550959667}
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