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Simplifying x2 = 11x + 21 Reorder the terms: x2 = 21 + 11x Solving x2 = 21 + 11x Solving for variable 'x'. Reorder the terms: -21 + -11x + x2 = 21 + 11x + -21 + -11x Reorder the terms: -21 + -11x + x2 = 21 + -21 + 11x + -11x Combine like terms: 21 + -21 = 0 -21 + -11x + x2 = 0 + 11x + -11x -21 + -11x + x2 = 11x + -11x Combine like terms: 11x + -11x = 0 -21 + -11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '21' to each side of the equation. -21 + -11x + 21 + x2 = 0 + 21 Reorder the terms: -21 + 21 + -11x + x2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + -11x + x2 = 0 + 21 -11x + x2 = 0 + 21 Combine like terms: 0 + 21 = 21 -11x + x2 = 21 The x term is -11x. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11x + 30.25 + x2 = 21 + 30.25 Reorder the terms: 30.25 + -11x + x2 = 21 + 30.25 Combine like terms: 21 + 30.25 = 51.25 30.25 + -11x + x2 = 51.25 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 51.25 Calculate the square root of the right side: 7.158910532 Break this problem into two subproblems by setting (x + -5.5) equal to 7.158910532 and -7.158910532.Subproblem 1
x + -5.5 = 7.158910532 Simplifying x + -5.5 = 7.158910532 Reorder the terms: -5.5 + x = 7.158910532 Solving -5.5 + x = 7.158910532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = 7.158910532 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 7.158910532 + 5.5 x = 7.158910532 + 5.5 Combine like terms: 7.158910532 + 5.5 = 12.658910532 x = 12.658910532 Simplifying x = 12.658910532Subproblem 2
x + -5.5 = -7.158910532 Simplifying x + -5.5 = -7.158910532 Reorder the terms: -5.5 + x = -7.158910532 Solving -5.5 + x = -7.158910532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = -7.158910532 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -7.158910532 + 5.5 x = -7.158910532 + 5.5 Combine like terms: -7.158910532 + 5.5 = -1.658910532 x = -1.658910532 Simplifying x = -1.658910532Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.658910532, -1.658910532}
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