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Simplifying x2 + 22x + 69 = 0 Reorder the terms: 69 + 22x + x2 = 0 Solving 69 + 22x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-69' to each side of the equation. 69 + 22x + -69 + x2 = 0 + -69 Reorder the terms: 69 + -69 + 22x + x2 = 0 + -69 Combine like terms: 69 + -69 = 0 0 + 22x + x2 = 0 + -69 22x + x2 = 0 + -69 Combine like terms: 0 + -69 = -69 22x + x2 = -69 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 = -69 + 121 Reorder the terms: 121 + 22x + x2 = -69 + 121 Combine like terms: -69 + 121 = 52 121 + 22x + x2 = 52 Factor a perfect square on the left side: (x + 11)(x + 11) = 52 Calculate the square root of the right side: 7.211102551 Break this problem into two subproblems by setting (x + 11) equal to 7.211102551 and -7.211102551.Subproblem 1
x + 11 = 7.211102551 Simplifying x + 11 = 7.211102551 Reorder the terms: 11 + x = 7.211102551 Solving 11 + x = 7.211102551 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 = 7.211102551 + -11 Combine like terms: 11 + -11 = 0 0 + x = 7.211102551 + -11 x = 7.211102551 + -11 Combine like terms: 7.211102551 + -11 = -3.788897449 x = -3.788897449 Simplifying x = -3.788897449Subproblem 2
x + 11 = -7.211102551 Simplifying x + 11 = -7.211102551 Reorder the terms: 11 + x = -7.211102551 Solving 11 + x = -7.211102551 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 = -7.211102551 + -11 Combine like terms: 11 + -11 = 0 0 + x = -7.211102551 + -11 x = -7.211102551 + -11 Combine like terms: -7.211102551 + -11 = -18.211102551 x = -18.211102551 Simplifying x = -18.211102551Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.788897449, -18.211102551}
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