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Simplifying x2 + 29x + 23 = 0 Reorder the terms: 23 + 29x + x2 = 0 Solving 23 + 29x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-23' to each side of the equation. 23 + 29x + -23 + x2 = 0 + -23 Reorder the terms: 23 + -23 + 29x + x2 = 0 + -23 Combine like terms: 23 + -23 = 0 0 + 29x + x2 = 0 + -23 29x + x2 = 0 + -23 Combine like terms: 0 + -23 = -23 29x + x2 = -23 The x term is 29x. Take half its coefficient (14.5). Square it (210.25) and add it to both sides. Add '210.25' to each side of the equation. 29x + 210.25 + x2 = -23 + 210.25 Reorder the terms: 210.25 + 29x + x2 = -23 + 210.25 Combine like terms: -23 + 210.25 = 187.25 210.25 + 29x + x2 = 187.25 Factor a perfect square on the left side: (x + 14.5)(x + 14.5) = 187.25 Calculate the square root of the right side: 13.683932183 Break this problem into two subproblems by setting (x + 14.5) equal to 13.683932183 and -13.683932183.Subproblem 1
x + 14.5 = 13.683932183 Simplifying x + 14.5 = 13.683932183 Reorder the terms: 14.5 + x = 13.683932183 Solving 14.5 + x = 13.683932183 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14.5' to each side of the equation. 14.5 + -14.5 + x = 13.683932183 + -14.5 Combine like terms: 14.5 + -14.5 = 0.0 0.0 + x = 13.683932183 + -14.5 x = 13.683932183 + -14.5 Combine like terms: 13.683932183 + -14.5 = -0.816067817 x = -0.816067817 Simplifying x = -0.816067817Subproblem 2
x + 14.5 = -13.683932183 Simplifying x + 14.5 = -13.683932183 Reorder the terms: 14.5 + x = -13.683932183 Solving 14.5 + x = -13.683932183 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14.5' to each side of the equation. 14.5 + -14.5 + x = -13.683932183 + -14.5 Combine like terms: 14.5 + -14.5 = 0.0 0.0 + x = -13.683932183 + -14.5 x = -13.683932183 + -14.5 Combine like terms: -13.683932183 + -14.5 = -28.183932183 x = -28.183932183 Simplifying x = -28.183932183Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.816067817, -28.183932183}
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