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Simplifying 344 = x2 + 2x Reorder the terms: 344 = 2x + x2 Solving 344 = 2x + x2 Solving for variable 'x'. Reorder the terms: 344 + -2x + -1x2 = 2x + -2x + x2 + -1x2 Combine like terms: 2x + -2x = 0 344 + -2x + -1x2 = 0 + x2 + -1x2 344 + -2x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 344 + -2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -344 + 2x + x2 = 0 Move the constant term to the right: Add '344' to each side of the equation. -344 + 2x + 344 + x2 = 0 + 344 Reorder the terms: -344 + 344 + 2x + x2 = 0 + 344 Combine like terms: -344 + 344 = 0 0 + 2x + x2 = 0 + 344 2x + x2 = 0 + 344 Combine like terms: 0 + 344 = 344 2x + x2 = 344 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 344 + 1 Reorder the terms: 1 + 2x + x2 = 344 + 1 Combine like terms: 344 + 1 = 345 1 + 2x + x2 = 345 Factor a perfect square on the left side: (x + 1)(x + 1) = 345 Calculate the square root of the right side: 18.574175621 Break this problem into two subproblems by setting (x + 1) equal to 18.574175621 and -18.574175621.Subproblem 1
x + 1 = 18.574175621 Simplifying x + 1 = 18.574175621 Reorder the terms: 1 + x = 18.574175621 Solving 1 + x = 18.574175621 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 18.574175621 + -1 Combine like terms: 1 + -1 = 0 0 + x = 18.574175621 + -1 x = 18.574175621 + -1 Combine like terms: 18.574175621 + -1 = 17.574175621 x = 17.574175621 Simplifying x = 17.574175621Subproblem 2
x + 1 = -18.574175621 Simplifying x + 1 = -18.574175621 Reorder the terms: 1 + x = -18.574175621 Solving 1 + x = -18.574175621 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -18.574175621 + -1 Combine like terms: 1 + -1 = 0 0 + x = -18.574175621 + -1 x = -18.574175621 + -1 Combine like terms: -18.574175621 + -1 = -19.574175621 x = -19.574175621 Simplifying x = -19.574175621Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.574175621, -19.574175621}
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