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Simplifying x2 + -22x = 9 Reorder the terms: -22x + x2 = 9 Solving -22x + x2 = 9 Solving for variable 'x'. Reorder the terms: -9 + -22x + x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + -22x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + -22x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + -22x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -22x + x2 = 0 + 9 -22x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 -22x + x2 = 9 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 = 9 + 121 Reorder the terms: 121 + -22x + x2 = 9 + 121 Combine like terms: 9 + 121 = 130 121 + -22x + x2 = 130 Factor a perfect square on the left side: (x + -11)(x + -11) = 130 Calculate the square root of the right side: 11.401754251 Break this problem into two subproblems by setting (x + -11) equal to 11.401754251 and -11.401754251.Subproblem 1
x + -11 = 11.401754251 Simplifying x + -11 = 11.401754251 Reorder the terms: -11 + x = 11.401754251 Solving -11 + x = 11.401754251 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 = 11.401754251 + 11 Combine like terms: -11 + 11 = 0 0 + x = 11.401754251 + 11 x = 11.401754251 + 11 Combine like terms: 11.401754251 + 11 = 22.401754251 x = 22.401754251 Simplifying x = 22.401754251Subproblem 2
x + -11 = -11.401754251 Simplifying x + -11 = -11.401754251 Reorder the terms: -11 + x = -11.401754251 Solving -11 + x = -11.401754251 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 = -11.401754251 + 11 Combine like terms: -11 + 11 = 0 0 + x = -11.401754251 + 11 x = -11.401754251 + 11 Combine like terms: -11.401754251 + 11 = -0.401754251 x = -0.401754251 Simplifying x = -0.401754251Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.401754251, -0.401754251}
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