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Simplifying x2 + -44x + 466 = 0 Reorder the terms: 466 + -44x + x2 = 0 Solving 466 + -44x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-466' to each side of the equation. 466 + -44x + -466 + x2 = 0 + -466 Reorder the terms: 466 + -466 + -44x + x2 = 0 + -466 Combine like terms: 466 + -466 = 0 0 + -44x + x2 = 0 + -466 -44x + x2 = 0 + -466 Combine like terms: 0 + -466 = -466 -44x + x2 = -466 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 = -466 + 484 Reorder the terms: 484 + -44x + x2 = -466 + 484 Combine like terms: -466 + 484 = 18 484 + -44x + x2 = 18 Factor a perfect square on the left side: (x + -22)(x + -22) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (x + -22) equal to 4.242640687 and -4.242640687.Subproblem 1
x + -22 = 4.242640687 Simplifying x + -22 = 4.242640687 Reorder the terms: -22 + x = 4.242640687 Solving -22 + x = 4.242640687 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 = 4.242640687 + 22 Combine like terms: -22 + 22 = 0 0 + x = 4.242640687 + 22 x = 4.242640687 + 22 Combine like terms: 4.242640687 + 22 = 26.242640687 x = 26.242640687 Simplifying x = 26.242640687Subproblem 2
x + -22 = -4.242640687 Simplifying x + -22 = -4.242640687 Reorder the terms: -22 + x = -4.242640687 Solving -22 + x = -4.242640687 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 = -4.242640687 + 22 Combine like terms: -22 + 22 = 0 0 + x = -4.242640687 + 22 x = -4.242640687 + 22 Combine like terms: -4.242640687 + 22 = 17.757359313 x = 17.757359313 Simplifying x = 17.757359313Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.242640687, 17.757359313}
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