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Simplifying x2 + 2x = 324 Reorder the terms: 2x + x2 = 324 Solving 2x + x2 = 324 Solving for variable 'x'. Reorder the terms: -324 + 2x + x2 = 324 + -324 Combine like terms: 324 + -324 = 0 -324 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '324' to each side of the equation. -324 + 2x + 324 + x2 = 0 + 324 Reorder the terms: -324 + 324 + 2x + x2 = 0 + 324 Combine like terms: -324 + 324 = 0 0 + 2x + x2 = 0 + 324 2x + x2 = 0 + 324 Combine like terms: 0 + 324 = 324 2x + x2 = 324 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 = 324 + 1 Reorder the terms: 1 + 2x + x2 = 324 + 1 Combine like terms: 324 + 1 = 325 1 + 2x + x2 = 325 Factor a perfect square on the left side: (x + 1)(x + 1) = 325 Calculate the square root of the right side: 18.027756377 Break this problem into two subproblems by setting (x + 1) equal to 18.027756377 and -18.027756377.Subproblem 1
x + 1 = 18.027756377 Simplifying x + 1 = 18.027756377 Reorder the terms: 1 + x = 18.027756377 Solving 1 + x = 18.027756377 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 = 18.027756377 + -1 Combine like terms: 1 + -1 = 0 0 + x = 18.027756377 + -1 x = 18.027756377 + -1 Combine like terms: 18.027756377 + -1 = 17.027756377 x = 17.027756377 Simplifying x = 17.027756377Subproblem 2
x + 1 = -18.027756377 Simplifying x + 1 = -18.027756377 Reorder the terms: 1 + x = -18.027756377 Solving 1 + x = -18.027756377 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 = -18.027756377 + -1 Combine like terms: 1 + -1 = 0 0 + x = -18.027756377 + -1 x = -18.027756377 + -1 Combine like terms: -18.027756377 + -1 = -19.027756377 x = -19.027756377 Simplifying x = -19.027756377Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.027756377, -19.027756377}
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