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Simplifying x2 + 23x + 39 = 0 Reorder the terms: 39 + 23x + x2 = 0 Solving 39 + 23x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-39' to each side of the equation. 39 + 23x + -39 + x2 = 0 + -39 Reorder the terms: 39 + -39 + 23x + x2 = 0 + -39 Combine like terms: 39 + -39 = 0 0 + 23x + x2 = 0 + -39 23x + x2 = 0 + -39 Combine like terms: 0 + -39 = -39 23x + x2 = -39 The x term is 23x. Take half its coefficient (11.5). Square it (132.25) and add it to both sides. Add '132.25' to each side of the equation. 23x + 132.25 + x2 = -39 + 132.25 Reorder the terms: 132.25 + 23x + x2 = -39 + 132.25 Combine like terms: -39 + 132.25 = 93.25 132.25 + 23x + x2 = 93.25 Factor a perfect square on the left side: (x + 11.5)(x + 11.5) = 93.25 Calculate the square root of the right side: 9.656603958 Break this problem into two subproblems by setting (x + 11.5) equal to 9.656603958 and -9.656603958.Subproblem 1
x + 11.5 = 9.656603958 Simplifying x + 11.5 = 9.656603958 Reorder the terms: 11.5 + x = 9.656603958 Solving 11.5 + x = 9.656603958 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.5' to each side of the equation. 11.5 + -11.5 + x = 9.656603958 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + x = 9.656603958 + -11.5 x = 9.656603958 + -11.5 Combine like terms: 9.656603958 + -11.5 = -1.843396042 x = -1.843396042 Simplifying x = -1.843396042Subproblem 2
x + 11.5 = -9.656603958 Simplifying x + 11.5 = -9.656603958 Reorder the terms: 11.5 + x = -9.656603958 Solving 11.5 + x = -9.656603958 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.5' to each side of the equation. 11.5 + -11.5 + x = -9.656603958 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + x = -9.656603958 + -11.5 x = -9.656603958 + -11.5 Combine like terms: -9.656603958 + -11.5 = -21.156603958 x = -21.156603958 Simplifying x = -21.156603958Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.843396042, -21.156603958}
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