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Simplifying x2 + 23x + 43 = 0 Reorder the terms: 43 + 23x + x2 = 0 Solving 43 + 23x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-43' to each side of the equation. 43 + 23x + -43 + x2 = 0 + -43 Reorder the terms: 43 + -43 + 23x + x2 = 0 + -43 Combine like terms: 43 + -43 = 0 0 + 23x + x2 = 0 + -43 23x + x2 = 0 + -43 Combine like terms: 0 + -43 = -43 23x + x2 = -43 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 = -43 + 132.25 Reorder the terms: 132.25 + 23x + x2 = -43 + 132.25 Combine like terms: -43 + 132.25 = 89.25 132.25 + 23x + x2 = 89.25 Factor a perfect square on the left side: (x + 11.5)(x + 11.5) = 89.25 Calculate the square root of the right side: 9.447221814 Break this problem into two subproblems by setting (x + 11.5) equal to 9.447221814 and -9.447221814.Subproblem 1
x + 11.5 = 9.447221814 Simplifying x + 11.5 = 9.447221814 Reorder the terms: 11.5 + x = 9.447221814 Solving 11.5 + x = 9.447221814 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 = 9.447221814 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + x = 9.447221814 + -11.5 x = 9.447221814 + -11.5 Combine like terms: 9.447221814 + -11.5 = -2.052778186 x = -2.052778186 Simplifying x = -2.052778186Subproblem 2
x + 11.5 = -9.447221814 Simplifying x + 11.5 = -9.447221814 Reorder the terms: 11.5 + x = -9.447221814 Solving 11.5 + x = -9.447221814 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 = -9.447221814 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + x = -9.447221814 + -11.5 x = -9.447221814 + -11.5 Combine like terms: -9.447221814 + -11.5 = -20.947221814 x = -20.947221814 Simplifying x = -20.947221814Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.052778186, -20.947221814}
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