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Simplifying x2 + 22x + -11 = 0 Reorder the terms: -11 + 22x + x2 = 0 Solving -11 + 22x + x2 = 0 Solving for variable 'x'. 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 = 0.489125293 x = 0.489125293 Simplifying x = 0.489125293Subproblem 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 = -22.489125293 x = -22.489125293 Simplifying x = -22.489125293Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.489125293, -22.489125293}
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