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Simplifying x2 + -11x + -11x + 121 = 21 Reorder the terms: 121 + -11x + -11x + x2 = 21 Combine like terms: -11x + -11x = -22x 121 + -22x + x2 = 21 Solving 121 + -22x + x2 = 21 Solving for variable 'x'. Reorder the terms: 121 + -21 + -22x + x2 = 21 + -21 Combine like terms: 121 + -21 = 100 100 + -22x + x2 = 21 + -21 Combine like terms: 21 + -21 = 0 100 + -22x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-100' to each side of the equation. 100 + -22x + -100 + x2 = 0 + -100 Reorder the terms: 100 + -100 + -22x + x2 = 0 + -100 Combine like terms: 100 + -100 = 0 0 + -22x + x2 = 0 + -100 -22x + x2 = 0 + -100 Combine like terms: 0 + -100 = -100 -22x + x2 = -100 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 = -100 + 121 Reorder the terms: 121 + -22x + x2 = -100 + 121 Combine like terms: -100 + 121 = 21 121 + -22x + x2 = 21 Factor a perfect square on the left side: (x + -11)(x + -11) = 21 Calculate the square root of the right side: 4.582575695 Break this problem into two subproblems by setting (x + -11) equal to 4.582575695 and -4.582575695.Subproblem 1
x + -11 = 4.582575695 Simplifying x + -11 = 4.582575695 Reorder the terms: -11 + x = 4.582575695 Solving -11 + x = 4.582575695 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 = 4.582575695 + 11 Combine like terms: -11 + 11 = 0 0 + x = 4.582575695 + 11 x = 4.582575695 + 11 Combine like terms: 4.582575695 + 11 = 15.582575695 x = 15.582575695 Simplifying x = 15.582575695Subproblem 2
x + -11 = -4.582575695 Simplifying x + -11 = -4.582575695 Reorder the terms: -11 + x = -4.582575695 Solving -11 + x = -4.582575695 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 = -4.582575695 + 11 Combine like terms: -11 + 11 = 0 0 + x = -4.582575695 + 11 x = -4.582575695 + 11 Combine like terms: -4.582575695 + 11 = 6.417424305 x = 6.417424305 Simplifying x = 6.417424305Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.582575695, 6.417424305}
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