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Simplifying x2 + -22x = 20 Reorder the terms: -22x + x2 = 20 Solving -22x + x2 = 20 Solving for variable 'x'. Reorder the terms: -20 + -22x + x2 = 20 + -20 Combine like terms: 20 + -20 = 0 -20 + -22x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '20' to each side of the equation. -20 + -22x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + -22x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -22x + x2 = 0 + 20 -22x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 -22x + x2 = 20 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 = 20 + 121 Reorder the terms: 121 + -22x + x2 = 20 + 121 Combine like terms: 20 + 121 = 141 121 + -22x + x2 = 141 Factor a perfect square on the left side: (x + -11)(x + -11) = 141 Calculate the square root of the right side: 11.874342087 Break this problem into two subproblems by setting (x + -11) equal to 11.874342087 and -11.874342087.Subproblem 1
x + -11 = 11.874342087 Simplifying x + -11 = 11.874342087 Reorder the terms: -11 + x = 11.874342087 Solving -11 + x = 11.874342087 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 = 11.874342087 + 11 Combine like terms: -11 + 11 = 0 0 + x = 11.874342087 + 11 x = 11.874342087 + 11 Combine like terms: 11.874342087 + 11 = 22.874342087 x = 22.874342087 Simplifying x = 22.874342087Subproblem 2
x + -11 = -11.874342087 Simplifying x + -11 = -11.874342087 Reorder the terms: -11 + x = -11.874342087 Solving -11 + x = -11.874342087 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 = -11.874342087 + 11 Combine like terms: -11 + 11 = 0 0 + x = -11.874342087 + 11 x = -11.874342087 + 11 Combine like terms: -11.874342087 + 11 = -0.874342087 x = -0.874342087 Simplifying x = -0.874342087Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.874342087, -0.874342087}
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