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Simplifying x2 + 25x + 23 = 0 Reorder the terms: 23 + 25x + x2 = 0 Solving 23 + 25x + 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 + 25x + -23 + x2 = 0 + -23 Reorder the terms: 23 + -23 + 25x + x2 = 0 + -23 Combine like terms: 23 + -23 = 0 0 + 25x + x2 = 0 + -23 25x + x2 = 0 + -23 Combine like terms: 0 + -23 = -23 25x + x2 = -23 The x term is 25x. Take half its coefficient (12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. 25x + 156.25 + x2 = -23 + 156.25 Reorder the terms: 156.25 + 25x + x2 = -23 + 156.25 Combine like terms: -23 + 156.25 = 133.25 156.25 + 25x + x2 = 133.25 Factor a perfect square on the left side: (x + 12.5)(x + 12.5) = 133.25 Calculate the square root of the right side: 11.543396381 Break this problem into two subproblems by setting (x + 12.5) equal to 11.543396381 and -11.543396381.Subproblem 1
x + 12.5 = 11.543396381 Simplifying x + 12.5 = 11.543396381 Reorder the terms: 12.5 + x = 11.543396381 Solving 12.5 + x = 11.543396381 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + x = 11.543396381 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = 11.543396381 + -12.5 x = 11.543396381 + -12.5 Combine like terms: 11.543396381 + -12.5 = -0.956603619 x = -0.956603619 Simplifying x = -0.956603619Subproblem 2
x + 12.5 = -11.543396381 Simplifying x + 12.5 = -11.543396381 Reorder the terms: 12.5 + x = -11.543396381 Solving 12.5 + x = -11.543396381 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + x = -11.543396381 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = -11.543396381 + -12.5 x = -11.543396381 + -12.5 Combine like terms: -11.543396381 + -12.5 = -24.043396381 x = -24.043396381 Simplifying x = -24.043396381Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.956603619, -24.043396381}
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