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Simplifying x2 + 22x = 15 Reorder the terms: 22x + x2 = 15 Solving 22x + x2 = 15 Solving for variable 'x'. Reorder the terms: -15 + 22x + x2 = 15 + -15 Combine like terms: 15 + -15 = 0 -15 + 22x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + 22x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + 22x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 22x + x2 = 0 + 15 22x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 22x + x2 = 15 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 = 15 + 121 Reorder the terms: 121 + 22x + x2 = 15 + 121 Combine like terms: 15 + 121 = 136 121 + 22x + x2 = 136 Factor a perfect square on the left side: (x + 11)(x + 11) = 136 Calculate the square root of the right side: 11.66190379 Break this problem into two subproblems by setting (x + 11) equal to 11.66190379 and -11.66190379.Subproblem 1
x + 11 = 11.66190379 Simplifying x + 11 = 11.66190379 Reorder the terms: 11 + x = 11.66190379 Solving 11 + x = 11.66190379 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 = 11.66190379 + -11 Combine like terms: 11 + -11 = 0 0 + x = 11.66190379 + -11 x = 11.66190379 + -11 Combine like terms: 11.66190379 + -11 = 0.66190379 x = 0.66190379 Simplifying x = 0.66190379Subproblem 2
x + 11 = -11.66190379 Simplifying x + 11 = -11.66190379 Reorder the terms: 11 + x = -11.66190379 Solving 11 + x = -11.66190379 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 = -11.66190379 + -11 Combine like terms: 11 + -11 = 0 0 + x = -11.66190379 + -11 x = -11.66190379 + -11 Combine like terms: -11.66190379 + -11 = -22.66190379 x = -22.66190379 Simplifying x = -22.66190379Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.66190379, -22.66190379}
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