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Simplifying 676 = 22x + x2 Solving 676 = 22x + x2 Solving for variable 'x'. Reorder the terms: 676 + -22x + -1x2 = 22x + -22x + x2 + -1x2 Combine like terms: 22x + -22x = 0 676 + -22x + -1x2 = 0 + x2 + -1x2 676 + -22x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 676 + -22x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -676 + 22x + x2 = 0 Move the constant term to the right: Add '676' to each side of the equation. -676 + 22x + 676 + x2 = 0 + 676 Reorder the terms: -676 + 676 + 22x + x2 = 0 + 676 Combine like terms: -676 + 676 = 0 0 + 22x + x2 = 0 + 676 22x + x2 = 0 + 676 Combine like terms: 0 + 676 = 676 22x + x2 = 676 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 = 676 + 121 Reorder the terms: 121 + 22x + x2 = 676 + 121 Combine like terms: 676 + 121 = 797 121 + 22x + x2 = 797 Factor a perfect square on the left side: (x + 11)(x + 11) = 797 Calculate the square root of the right side: 28.231188427 Break this problem into two subproblems by setting (x + 11) equal to 28.231188427 and -28.231188427.Subproblem 1
x + 11 = 28.231188427 Simplifying x + 11 = 28.231188427 Reorder the terms: 11 + x = 28.231188427 Solving 11 + x = 28.231188427 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 = 28.231188427 + -11 Combine like terms: 11 + -11 = 0 0 + x = 28.231188427 + -11 x = 28.231188427 + -11 Combine like terms: 28.231188427 + -11 = 17.231188427 x = 17.231188427 Simplifying x = 17.231188427Subproblem 2
x + 11 = -28.231188427 Simplifying x + 11 = -28.231188427 Reorder the terms: 11 + x = -28.231188427 Solving 11 + x = -28.231188427 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 = -28.231188427 + -11 Combine like terms: 11 + -11 = 0 0 + x = -28.231188427 + -11 x = -28.231188427 + -11 Combine like terms: -28.231188427 + -11 = -39.231188427 x = -39.231188427 Simplifying x = -39.231188427Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.231188427, -39.231188427}
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