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Simplifying x2 + x2 + -324 = x2 + 2x + 1 Reorder the terms: -324 + x2 + x2 = x2 + 2x + 1 Combine like terms: x2 + x2 = 2x2 -324 + 2x2 = x2 + 2x + 1 Reorder the terms: -324 + 2x2 = 1 + 2x + x2 Solving -324 + 2x2 = 1 + 2x + x2 Solving for variable 'x'. Reorder the terms: -324 + -1 + -2x + 2x2 + -1x2 = 1 + 2x + x2 + -1 + -2x + -1x2 Combine like terms: -324 + -1 = -325 -325 + -2x + 2x2 + -1x2 = 1 + 2x + x2 + -1 + -2x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 -325 + -2x + 1x2 = 1 + 2x + x2 + -1 + -2x + -1x2 Reorder the terms: -325 + -2x + 1x2 = 1 + -1 + 2x + -2x + x2 + -1x2 Combine like terms: 1 + -1 = 0 -325 + -2x + 1x2 = 0 + 2x + -2x + x2 + -1x2 -325 + -2x + 1x2 = 2x + -2x + x2 + -1x2 Combine like terms: 2x + -2x = 0 -325 + -2x + 1x2 = 0 + x2 + -1x2 -325 + -2x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -325 + -2x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '325' to each side of the equation. -325 + -2x + 325 + x2 = 0 + 325 Reorder the terms: -325 + 325 + -2x + x2 = 0 + 325 Combine like terms: -325 + 325 = 0 0 + -2x + x2 = 0 + 325 -2x + x2 = 0 + 325 Combine like terms: 0 + 325 = 325 -2x + x2 = 325 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 = 325 + 1 Reorder the terms: 1 + -2x + x2 = 325 + 1 Combine like terms: 325 + 1 = 326 1 + -2x + x2 = 326 Factor a perfect square on the left side: (x + -1)(x + -1) = 326 Calculate the square root of the right side: 18.055470085 Break this problem into two subproblems by setting (x + -1) equal to 18.055470085 and -18.055470085.Subproblem 1
x + -1 = 18.055470085 Simplifying x + -1 = 18.055470085 Reorder the terms: -1 + x = 18.055470085 Solving -1 + x = 18.055470085 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 = 18.055470085 + 1 Combine like terms: -1 + 1 = 0 0 + x = 18.055470085 + 1 x = 18.055470085 + 1 Combine like terms: 18.055470085 + 1 = 19.055470085 x = 19.055470085 Simplifying x = 19.055470085Subproblem 2
x + -1 = -18.055470085 Simplifying x + -1 = -18.055470085 Reorder the terms: -1 + x = -18.055470085 Solving -1 + x = -18.055470085 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 = -18.055470085 + 1 Combine like terms: -1 + 1 = 0 0 + x = -18.055470085 + 1 x = -18.055470085 + 1 Combine like terms: -18.055470085 + 1 = -17.055470085 x = -17.055470085 Simplifying x = -17.055470085Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.055470085, -17.055470085}
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