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Simplifying x2 + -22x = 100 Reorder the terms: -22x + x2 = 100 Solving -22x + x2 = 100 Solving for variable 'x'. Reorder the terms: -100 + -22x + x2 = 100 + -100 Combine like terms: 100 + -100 = 0 -100 + -22x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '100' to each side of the equation. -100 + -22x + 100 + x2 = 0 + 100 Reorder the terms: -100 + 100 + -22x + x2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + -22x + x2 = 0 + 100 -22x + x2 = 0 + 100 Combine like terms: 0 + 100 = 100 -22x + x2 = 100 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 = 100 + 121 Reorder the terms: 121 + -22x + x2 = 100 + 121 Combine like terms: 100 + 121 = 221 121 + -22x + x2 = 221 Factor a perfect square on the left side: (x + -11)(x + -11) = 221 Calculate the square root of the right side: 14.866068747 Break this problem into two subproblems by setting (x + -11) equal to 14.866068747 and -14.866068747.Subproblem 1
x + -11 = 14.866068747 Simplifying x + -11 = 14.866068747 Reorder the terms: -11 + x = 14.866068747 Solving -11 + x = 14.866068747 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 = 14.866068747 + 11 Combine like terms: -11 + 11 = 0 0 + x = 14.866068747 + 11 x = 14.866068747 + 11 Combine like terms: 14.866068747 + 11 = 25.866068747 x = 25.866068747 Simplifying x = 25.866068747Subproblem 2
x + -11 = -14.866068747 Simplifying x + -11 = -14.866068747 Reorder the terms: -11 + x = -14.866068747 Solving -11 + x = -14.866068747 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 = -14.866068747 + 11 Combine like terms: -11 + 11 = 0 0 + x = -14.866068747 + 11 x = -14.866068747 + 11 Combine like terms: -14.866068747 + 11 = -3.866068747 x = -3.866068747 Simplifying x = -3.866068747Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.866068747, -3.866068747}
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