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Simplifying x2 + 22x = 50 Reorder the terms: 22x + x2 = 50 Solving 22x + x2 = 50 Solving for variable 'x'. Reorder the terms: -50 + 22x + x2 = 50 + -50 Combine like terms: 50 + -50 = 0 -50 + 22x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '50' to each side of the equation. -50 + 22x + 50 + x2 = 0 + 50 Reorder the terms: -50 + 50 + 22x + x2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + 22x + x2 = 0 + 50 22x + x2 = 0 + 50 Combine like terms: 0 + 50 = 50 22x + x2 = 50 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 = 50 + 121 Reorder the terms: 121 + 22x + x2 = 50 + 121 Combine like terms: 50 + 121 = 171 121 + 22x + x2 = 171 Factor a perfect square on the left side: (x + 11)(x + 11) = 171 Calculate the square root of the right side: 13.076696831 Break this problem into two subproblems by setting (x + 11) equal to 13.076696831 and -13.076696831.Subproblem 1
x + 11 = 13.076696831 Simplifying x + 11 = 13.076696831 Reorder the terms: 11 + x = 13.076696831 Solving 11 + x = 13.076696831 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 = 13.076696831 + -11 Combine like terms: 11 + -11 = 0 0 + x = 13.076696831 + -11 x = 13.076696831 + -11 Combine like terms: 13.076696831 + -11 = 2.076696831 x = 2.076696831 Simplifying x = 2.076696831Subproblem 2
x + 11 = -13.076696831 Simplifying x + 11 = -13.076696831 Reorder the terms: 11 + x = -13.076696831 Solving 11 + x = -13.076696831 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 = -13.076696831 + -11 Combine like terms: 11 + -11 = 0 0 + x = -13.076696831 + -11 x = -13.076696831 + -11 Combine like terms: -13.076696831 + -11 = -24.076696831 x = -24.076696831 Simplifying x = -24.076696831Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.076696831, -24.076696831}
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