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Simplifying 324 = (x + 22) * x + 7 Reorder the terms: 324 = (22 + x) * x + 7 Reorder the terms for easier multiplication: 324 = x(22 + x) + 7 324 = (22 * x + x * x) + 7 324 = (22x + x2) + 7 Reorder the terms: 324 = 7 + 22x + x2 Solving 324 = 7 + 22x + x2 Solving for variable 'x'. Combine like terms: 324 + -7 = 317 317 + -22x + -1x2 = 7 + 22x + x2 + -7 + -22x + -1x2 Reorder the terms: 317 + -22x + -1x2 = 7 + -7 + 22x + -22x + x2 + -1x2 Combine like terms: 7 + -7 = 0 317 + -22x + -1x2 = 0 + 22x + -22x + x2 + -1x2 317 + -22x + -1x2 = 22x + -22x + x2 + -1x2 Combine like terms: 22x + -22x = 0 317 + -22x + -1x2 = 0 + x2 + -1x2 317 + -22x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 317 + -22x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -317 + 22x + x2 = 0 Move the constant term to the right: Add '317' to each side of the equation. -317 + 22x + 317 + x2 = 0 + 317 Reorder the terms: -317 + 317 + 22x + x2 = 0 + 317 Combine like terms: -317 + 317 = 0 0 + 22x + x2 = 0 + 317 22x + x2 = 0 + 317 Combine like terms: 0 + 317 = 317 22x + x2 = 317 The x term is 22x. Take half its coefficient (11). Square it (121) and add it to both sides. Add '121' to each side of the equation. 22x + 121 + x2 = 317 + 121 Reorder the terms: 121 + 22x + x2 = 317 + 121 Combine like terms: 317 + 121 = 438 121 + 22x + x2 = 438 Factor a perfect square on the left side: (x + 11)(x + 11) = 438 Calculate the square root of the right side: 20.928449536 Break this problem into two subproblems by setting (x + 11) equal to 20.928449536 and -20.928449536.Subproblem 1
x + 11 = 20.928449536 Simplifying x + 11 = 20.928449536 Reorder the terms: 11 + x = 20.928449536 Solving 11 + x = 20.928449536 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x = 20.928449536 + -11 Combine like terms: 11 + -11 = 0 0 + x = 20.928449536 + -11 x = 20.928449536 + -11 Combine like terms: 20.928449536 + -11 = 9.928449536 x = 9.928449536 Simplifying x = 9.928449536Subproblem 2
x + 11 = -20.928449536 Simplifying x + 11 = -20.928449536 Reorder the terms: 11 + x = -20.928449536 Solving 11 + x = -20.928449536 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x = -20.928449536 + -11 Combine like terms: 11 + -11 = 0 0 + x = -20.928449536 + -11 x = -20.928449536 + -11 Combine like terms: -20.928449536 + -11 = -31.928449536 x = -31.928449536 Simplifying x = -31.928449536Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.928449536, -31.928449536}
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