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Simplifying x2 + 22x = 24 Reorder the terms: 22x + x2 = 24 Solving 22x + x2 = 24 Solving for variable 'x'. Reorder the terms: -24 + 22x + x2 = 24 + -24 Combine like terms: 24 + -24 = 0 -24 + 22x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '24' to each side of the equation. -24 + 22x + 24 + x2 = 0 + 24 Reorder the terms: -24 + 24 + 22x + x2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + 22x + x2 = 0 + 24 22x + x2 = 0 + 24 Combine like terms: 0 + 24 = 24 22x + x2 = 24 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 = 24 + 121 Reorder the terms: 121 + 22x + x2 = 24 + 121 Combine like terms: 24 + 121 = 145 121 + 22x + x2 = 145 Factor a perfect square on the left side: (x + 11)(x + 11) = 145 Calculate the square root of the right side: 12.041594579 Break this problem into two subproblems by setting (x + 11) equal to 12.041594579 and -12.041594579.Subproblem 1
x + 11 = 12.041594579 Simplifying x + 11 = 12.041594579 Reorder the terms: 11 + x = 12.041594579 Solving 11 + x = 12.041594579 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 = 12.041594579 + -11 Combine like terms: 11 + -11 = 0 0 + x = 12.041594579 + -11 x = 12.041594579 + -11 Combine like terms: 12.041594579 + -11 = 1.041594579 x = 1.041594579 Simplifying x = 1.041594579Subproblem 2
x + 11 = -12.041594579 Simplifying x + 11 = -12.041594579 Reorder the terms: 11 + x = -12.041594579 Solving 11 + x = -12.041594579 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 = -12.041594579 + -11 Combine like terms: 11 + -11 = 0 0 + x = -12.041594579 + -11 x = -12.041594579 + -11 Combine like terms: -12.041594579 + -11 = -23.041594579 x = -23.041594579 Simplifying x = -23.041594579Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.041594579, -23.041594579}
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