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Simplifying 25x2 + -34x + -343 = 0 Reorder the terms: -343 + -34x + 25x2 = 0 Solving -343 + -34x + 25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -13.72 + -1.36x + x2 = 0 Move the constant term to the right: Add '13.72' to each side of the equation. -13.72 + -1.36x + 13.72 + x2 = 0 + 13.72 Reorder the terms: -13.72 + 13.72 + -1.36x + x2 = 0 + 13.72 Combine like terms: -13.72 + 13.72 = 0.00 0.00 + -1.36x + x2 = 0 + 13.72 -1.36x + x2 = 0 + 13.72 Combine like terms: 0 + 13.72 = 13.72 -1.36x + x2 = 13.72 The x term is -1.36x. Take half its coefficient (-0.68). Square it (0.4624) and add it to both sides. Add '0.4624' to each side of the equation. -1.36x + 0.4624 + x2 = 13.72 + 0.4624 Reorder the terms: 0.4624 + -1.36x + x2 = 13.72 + 0.4624 Combine like terms: 13.72 + 0.4624 = 14.1824 0.4624 + -1.36x + x2 = 14.1824 Factor a perfect square on the left side: (x + -0.68)(x + -0.68) = 14.1824 Calculate the square root of the right side: 3.765952735 Break this problem into two subproblems by setting (x + -0.68) equal to 3.765952735 and -3.765952735.Subproblem 1
x + -0.68 = 3.765952735 Simplifying x + -0.68 = 3.765952735 Reorder the terms: -0.68 + x = 3.765952735 Solving -0.68 + x = 3.765952735 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.68' to each side of the equation. -0.68 + 0.68 + x = 3.765952735 + 0.68 Combine like terms: -0.68 + 0.68 = 0.00 0.00 + x = 3.765952735 + 0.68 x = 3.765952735 + 0.68 Combine like terms: 3.765952735 + 0.68 = 4.445952735 x = 4.445952735 Simplifying x = 4.445952735Subproblem 2
x + -0.68 = -3.765952735 Simplifying x + -0.68 = -3.765952735 Reorder the terms: -0.68 + x = -3.765952735 Solving -0.68 + x = -3.765952735 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.68' to each side of the equation. -0.68 + 0.68 + x = -3.765952735 + 0.68 Combine like terms: -0.68 + 0.68 = 0.00 0.00 + x = -3.765952735 + 0.68 x = -3.765952735 + 0.68 Combine like terms: -3.765952735 + 0.68 = -3.085952735 x = -3.085952735 Simplifying x = -3.085952735Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.445952735, -3.085952735}
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