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Simplifying x2 + -6x = 325 Reorder the terms: -6x + x2 = 325 Solving -6x + x2 = 325 Solving for variable 'x'. Reorder the terms: -325 + -6x + x2 = 325 + -325 Combine like terms: 325 + -325 = 0 -325 + -6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '325' to each side of the equation. -325 + -6x + 325 + x2 = 0 + 325 Reorder the terms: -325 + 325 + -6x + x2 = 0 + 325 Combine like terms: -325 + 325 = 0 0 + -6x + x2 = 0 + 325 -6x + x2 = 0 + 325 Combine like terms: 0 + 325 = 325 -6x + x2 = 325 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 325 + 9 Reorder the terms: 9 + -6x + x2 = 325 + 9 Combine like terms: 325 + 9 = 334 9 + -6x + x2 = 334 Factor a perfect square on the left side: (x + -3)(x + -3) = 334 Calculate the square root of the right side: 18.275666882 Break this problem into two subproblems by setting (x + -3) equal to 18.275666882 and -18.275666882.Subproblem 1
x + -3 = 18.275666882 Simplifying x + -3 = 18.275666882 Reorder the terms: -3 + x = 18.275666882 Solving -3 + x = 18.275666882 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 18.275666882 + 3 Combine like terms: -3 + 3 = 0 0 + x = 18.275666882 + 3 x = 18.275666882 + 3 Combine like terms: 18.275666882 + 3 = 21.275666882 x = 21.275666882 Simplifying x = 21.275666882Subproblem 2
x + -3 = -18.275666882 Simplifying x + -3 = -18.275666882 Reorder the terms: -3 + x = -18.275666882 Solving -3 + x = -18.275666882 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -18.275666882 + 3 Combine like terms: -3 + 3 = 0 0 + x = -18.275666882 + 3 x = -18.275666882 + 3 Combine like terms: -18.275666882 + 3 = -15.275666882 x = -15.275666882 Simplifying x = -15.275666882Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.275666882, -15.275666882}
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