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Simplifying (x + -22)(x + -22) + -27 = 0 Reorder the terms: (-22 + x)(x + -22) + -27 = 0 Reorder the terms: (-22 + x)(-22 + x) + -27 = 0 Multiply (-22 + x) * (-22 + x) (-22(-22 + x) + x(-22 + x)) + -27 = 0 ((-22 * -22 + x * -22) + x(-22 + x)) + -27 = 0 ((484 + -22x) + x(-22 + x)) + -27 = 0 (484 + -22x + (-22 * x + x * x)) + -27 = 0 (484 + -22x + (-22x + x2)) + -27 = 0 Combine like terms: -22x + -22x = -44x (484 + -44x + x2) + -27 = 0 Reorder the terms: 484 + -27 + -44x + x2 = 0 Combine like terms: 484 + -27 = 457 457 + -44x + x2 = 0 Solving 457 + -44x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-457' to each side of the equation. 457 + -44x + -457 + x2 = 0 + -457 Reorder the terms: 457 + -457 + -44x + x2 = 0 + -457 Combine like terms: 457 + -457 = 0 0 + -44x + x2 = 0 + -457 -44x + x2 = 0 + -457 Combine like terms: 0 + -457 = -457 -44x + x2 = -457 The x term is -44x. Take half its coefficient (-22). Square it (484) and add it to both sides. Add '484' to each side of the equation. -44x + 484 + x2 = -457 + 484 Reorder the terms: 484 + -44x + x2 = -457 + 484 Combine like terms: -457 + 484 = 27 484 + -44x + x2 = 27 Factor a perfect square on the left side: (x + -22)(x + -22) = 27 Calculate the square root of the right side: 5.196152423 Break this problem into two subproblems by setting (x + -22) equal to 5.196152423 and -5.196152423.Subproblem 1
x + -22 = 5.196152423 Simplifying x + -22 = 5.196152423 Reorder the terms: -22 + x = 5.196152423 Solving -22 + x = 5.196152423 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22' to each side of the equation. -22 + 22 + x = 5.196152423 + 22 Combine like terms: -22 + 22 = 0 0 + x = 5.196152423 + 22 x = 5.196152423 + 22 Combine like terms: 5.196152423 + 22 = 27.196152423 x = 27.196152423 Simplifying x = 27.196152423Subproblem 2
x + -22 = -5.196152423 Simplifying x + -22 = -5.196152423 Reorder the terms: -22 + x = -5.196152423 Solving -22 + x = -5.196152423 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22' to each side of the equation. -22 + 22 + x = -5.196152423 + 22 Combine like terms: -22 + 22 = 0 0 + x = -5.196152423 + 22 x = -5.196152423 + 22 Combine like terms: -5.196152423 + 22 = 16.803847577 x = 16.803847577 Simplifying x = 16.803847577Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.196152423, 16.803847577}
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