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Simplifying x2 + -22x = 11 Reorder the terms: -22x + x2 = 11 Solving -22x + x2 = 11 Solving for variable 'x'. Reorder the terms: -11 + -22x + x2 = 11 + -11 Combine like terms: 11 + -11 = 0 -11 + -22x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + -22x + 11 + x2 = 0 + 11 Reorder the terms: -11 + 11 + -22x + x2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -22x + x2 = 0 + 11 -22x + x2 = 0 + 11 Combine like terms: 0 + 11 = 11 -22x + x2 = 11 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 = 11 + 121 Reorder the terms: 121 + -22x + x2 = 11 + 121 Combine like terms: 11 + 121 = 132 121 + -22x + x2 = 132 Factor a perfect square on the left side: (x + -11)(x + -11) = 132 Calculate the square root of the right side: 11.489125293 Break this problem into two subproblems by setting (x + -11) equal to 11.489125293 and -11.489125293.Subproblem 1
x + -11 = 11.489125293 Simplifying x + -11 = 11.489125293 Reorder the terms: -11 + x = 11.489125293 Solving -11 + x = 11.489125293 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 = 11.489125293 + 11 Combine like terms: -11 + 11 = 0 0 + x = 11.489125293 + 11 x = 11.489125293 + 11 Combine like terms: 11.489125293 + 11 = 22.489125293 x = 22.489125293 Simplifying x = 22.489125293Subproblem 2
x + -11 = -11.489125293 Simplifying x + -11 = -11.489125293 Reorder the terms: -11 + x = -11.489125293 Solving -11 + x = -11.489125293 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 = -11.489125293 + 11 Combine like terms: -11 + 11 = 0 0 + x = -11.489125293 + 11 x = -11.489125293 + 11 Combine like terms: -11.489125293 + 11 = -0.489125293 x = -0.489125293 Simplifying x = -0.489125293Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.489125293, -0.489125293}
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