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Simplifying x(x + 2) = 342 Reorder the terms: x(2 + x) = 342 (2 * x + x * x) = 342 (2x + x2) = 342 Solving 2x + x2 = 342 Solving for variable 'x'. Reorder the terms: -342 + 2x + x2 = 342 + -342 Combine like terms: 342 + -342 = 0 -342 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '342' to each side of the equation. -342 + 2x + 342 + x2 = 0 + 342 Reorder the terms: -342 + 342 + 2x + x2 = 0 + 342 Combine like terms: -342 + 342 = 0 0 + 2x + x2 = 0 + 342 2x + x2 = 0 + 342 Combine like terms: 0 + 342 = 342 2x + x2 = 342 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 = 342 + 1 Reorder the terms: 1 + 2x + x2 = 342 + 1 Combine like terms: 342 + 1 = 343 1 + 2x + x2 = 343 Factor a perfect square on the left side: (x + 1)(x + 1) = 343 Calculate the square root of the right side: 18.520259177 Break this problem into two subproblems by setting (x + 1) equal to 18.520259177 and -18.520259177.Subproblem 1
x + 1 = 18.520259177 Simplifying x + 1 = 18.520259177 Reorder the terms: 1 + x = 18.520259177 Solving 1 + x = 18.520259177 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 = 18.520259177 + -1 Combine like terms: 1 + -1 = 0 0 + x = 18.520259177 + -1 x = 18.520259177 + -1 Combine like terms: 18.520259177 + -1 = 17.520259177 x = 17.520259177 Simplifying x = 17.520259177Subproblem 2
x + 1 = -18.520259177 Simplifying x + 1 = -18.520259177 Reorder the terms: 1 + x = -18.520259177 Solving 1 + x = -18.520259177 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 = -18.520259177 + -1 Combine like terms: 1 + -1 = 0 0 + x = -18.520259177 + -1 x = -18.520259177 + -1 Combine like terms: -18.520259177 + -1 = -19.520259177 x = -19.520259177 Simplifying x = -19.520259177Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.520259177, -19.520259177}
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