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Simplifying x2 + -22x + 121 = 90 Reorder the terms: 121 + -22x + x2 = 90 Solving 121 + -22x + x2 = 90 Solving for variable 'x'. Reorder the terms: 121 + -90 + -22x + x2 = 90 + -90 Combine like terms: 121 + -90 = 31 31 + -22x + x2 = 90 + -90 Combine like terms: 90 + -90 = 0 31 + -22x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-31' to each side of the equation. 31 + -22x + -31 + x2 = 0 + -31 Reorder the terms: 31 + -31 + -22x + x2 = 0 + -31 Combine like terms: 31 + -31 = 0 0 + -22x + x2 = 0 + -31 -22x + x2 = 0 + -31 Combine like terms: 0 + -31 = -31 -22x + x2 = -31 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 = -31 + 121 Reorder the terms: 121 + -22x + x2 = -31 + 121 Combine like terms: -31 + 121 = 90 121 + -22x + x2 = 90 Factor a perfect square on the left side: (x + -11)(x + -11) = 90 Calculate the square root of the right side: 9.486832981 Break this problem into two subproblems by setting (x + -11) equal to 9.486832981 and -9.486832981.Subproblem 1
x + -11 = 9.486832981 Simplifying x + -11 = 9.486832981 Reorder the terms: -11 + x = 9.486832981 Solving -11 + x = 9.486832981 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 = 9.486832981 + 11 Combine like terms: -11 + 11 = 0 0 + x = 9.486832981 + 11 x = 9.486832981 + 11 Combine like terms: 9.486832981 + 11 = 20.486832981 x = 20.486832981 Simplifying x = 20.486832981Subproblem 2
x + -11 = -9.486832981 Simplifying x + -11 = -9.486832981 Reorder the terms: -11 + x = -9.486832981 Solving -11 + x = -9.486832981 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 = -9.486832981 + 11 Combine like terms: -11 + 11 = 0 0 + x = -9.486832981 + 11 x = -9.486832981 + 11 Combine like terms: -9.486832981 + 11 = 1.513167019 x = 1.513167019 Simplifying x = 1.513167019Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.486832981, 1.513167019}
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