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Simplifying (x + -22)(x + -22) = 12 Reorder the terms: (-22 + x)(x + -22) = 12 Reorder the terms: (-22 + x)(-22 + x) = 12 Multiply (-22 + x) * (-22 + x) (-22(-22 + x) + x(-22 + x)) = 12 ((-22 * -22 + x * -22) + x(-22 + x)) = 12 ((484 + -22x) + x(-22 + x)) = 12 (484 + -22x + (-22 * x + x * x)) = 12 (484 + -22x + (-22x + x2)) = 12 Combine like terms: -22x + -22x = -44x (484 + -44x + x2) = 12 Solving 484 + -44x + x2 = 12 Solving for variable 'x'. Reorder the terms: 484 + -12 + -44x + x2 = 12 + -12 Combine like terms: 484 + -12 = 472 472 + -44x + x2 = 12 + -12 Combine like terms: 12 + -12 = 0 472 + -44x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-472' to each side of the equation. 472 + -44x + -472 + x2 = 0 + -472 Reorder the terms: 472 + -472 + -44x + x2 = 0 + -472 Combine like terms: 472 + -472 = 0 0 + -44x + x2 = 0 + -472 -44x + x2 = 0 + -472 Combine like terms: 0 + -472 = -472 -44x + x2 = -472 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 = -472 + 484 Reorder the terms: 484 + -44x + x2 = -472 + 484 Combine like terms: -472 + 484 = 12 484 + -44x + x2 = 12 Factor a perfect square on the left side: (x + -22)(x + -22) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (x + -22) equal to 3.464101615 and -3.464101615.Subproblem 1
x + -22 = 3.464101615 Simplifying x + -22 = 3.464101615 Reorder the terms: -22 + x = 3.464101615 Solving -22 + x = 3.464101615 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 = 3.464101615 + 22 Combine like terms: -22 + 22 = 0 0 + x = 3.464101615 + 22 x = 3.464101615 + 22 Combine like terms: 3.464101615 + 22 = 25.464101615 x = 25.464101615 Simplifying x = 25.464101615Subproblem 2
x + -22 = -3.464101615 Simplifying x + -22 = -3.464101615 Reorder the terms: -22 + x = -3.464101615 Solving -22 + x = -3.464101615 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 = -3.464101615 + 22 Combine like terms: -22 + 22 = 0 0 + x = -3.464101615 + 22 x = -3.464101615 + 22 Combine like terms: -3.464101615 + 22 = 18.535898385 x = 18.535898385 Simplifying x = 18.535898385Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.464101615, 18.535898385}
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