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Simplifying 334 = x2 + 2x Reorder the terms: 334 = 2x + x2 Solving 334 = 2x + x2 Solving for variable 'x'. Reorder the terms: 334 + -2x + -1x2 = 2x + -2x + x2 + -1x2 Combine like terms: 2x + -2x = 0 334 + -2x + -1x2 = 0 + x2 + -1x2 334 + -2x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 334 + -2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -334 + 2x + x2 = 0 Move the constant term to the right: Add '334' to each side of the equation. -334 + 2x + 334 + x2 = 0 + 334 Reorder the terms: -334 + 334 + 2x + x2 = 0 + 334 Combine like terms: -334 + 334 = 0 0 + 2x + x2 = 0 + 334 2x + x2 = 0 + 334 Combine like terms: 0 + 334 = 334 2x + x2 = 334 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 = 334 + 1 Reorder the terms: 1 + 2x + x2 = 334 + 1 Combine like terms: 334 + 1 = 335 1 + 2x + x2 = 335 Factor a perfect square on the left side: (x + 1)(x + 1) = 335 Calculate the square root of the right side: 18.303005218 Break this problem into two subproblems by setting (x + 1) equal to 18.303005218 and -18.303005218.Subproblem 1
x + 1 = 18.303005218 Simplifying x + 1 = 18.303005218 Reorder the terms: 1 + x = 18.303005218 Solving 1 + x = 18.303005218 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 = 18.303005218 + -1 Combine like terms: 1 + -1 = 0 0 + x = 18.303005218 + -1 x = 18.303005218 + -1 Combine like terms: 18.303005218 + -1 = 17.303005218 x = 17.303005218 Simplifying x = 17.303005218Subproblem 2
x + 1 = -18.303005218 Simplifying x + 1 = -18.303005218 Reorder the terms: 1 + x = -18.303005218 Solving 1 + x = -18.303005218 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 = -18.303005218 + -1 Combine like terms: 1 + -1 = 0 0 + x = -18.303005218 + -1 x = -18.303005218 + -1 Combine like terms: -18.303005218 + -1 = -19.303005218 x = -19.303005218 Simplifying x = -19.303005218Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.303005218, -19.303005218}
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