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Simplifying 326 = x(x + 2) Reorder the terms: 326 = x(2 + x) 326 = (2 * x + x * x) 326 = (2x + x2) Solving 326 = 2x + x2 Solving for variable 'x'. Reorder the terms: 326 + -2x + -1x2 = 2x + -2x + x2 + -1x2 Combine like terms: 2x + -2x = 0 326 + -2x + -1x2 = 0 + x2 + -1x2 326 + -2x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 326 + -2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -326 + 2x + x2 = 0 Move the constant term to the right: Add '326' to each side of the equation. -326 + 2x + 326 + x2 = 0 + 326 Reorder the terms: -326 + 326 + 2x + x2 = 0 + 326 Combine like terms: -326 + 326 = 0 0 + 2x + x2 = 0 + 326 2x + x2 = 0 + 326 Combine like terms: 0 + 326 = 326 2x + x2 = 326 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 = 326 + 1 Reorder the terms: 1 + 2x + x2 = 326 + 1 Combine like terms: 326 + 1 = 327 1 + 2x + x2 = 327 Factor a perfect square on the left side: (x + 1)(x + 1) = 327 Calculate the square root of the right side: 18.08314132 Break this problem into two subproblems by setting (x + 1) equal to 18.08314132 and -18.08314132.Subproblem 1
x + 1 = 18.08314132 Simplifying x + 1 = 18.08314132 Reorder the terms: 1 + x = 18.08314132 Solving 1 + x = 18.08314132 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 = 18.08314132 + -1 Combine like terms: 1 + -1 = 0 0 + x = 18.08314132 + -1 x = 18.08314132 + -1 Combine like terms: 18.08314132 + -1 = 17.08314132 x = 17.08314132 Simplifying x = 17.08314132Subproblem 2
x + 1 = -18.08314132 Simplifying x + 1 = -18.08314132 Reorder the terms: 1 + x = -18.08314132 Solving 1 + x = -18.08314132 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 = -18.08314132 + -1 Combine like terms: 1 + -1 = 0 0 + x = -18.08314132 + -1 x = -18.08314132 + -1 Combine like terms: -18.08314132 + -1 = -19.08314132 x = -19.08314132 Simplifying x = -19.08314132Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.08314132, -19.08314132}
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