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Simplifying x2 + 25x + -431 = 0 Reorder the terms: -431 + 25x + x2 = 0 Solving -431 + 25x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '431' to each side of the equation. -431 + 25x + 431 + x2 = 0 + 431 Reorder the terms: -431 + 431 + 25x + x2 = 0 + 431 Combine like terms: -431 + 431 = 0 0 + 25x + x2 = 0 + 431 25x + x2 = 0 + 431 Combine like terms: 0 + 431 = 431 25x + x2 = 431 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 = 431 + 156.25 Reorder the terms: 156.25 + 25x + x2 = 431 + 156.25 Combine like terms: 431 + 156.25 = 587.25 156.25 + 25x + x2 = 587.25 Factor a perfect square on the left side: (x + 12.5)(x + 12.5) = 587.25 Calculate the square root of the right side: 24.233241632 Break this problem into two subproblems by setting (x + 12.5) equal to 24.233241632 and -24.233241632.Subproblem 1
x + 12.5 = 24.233241632 Simplifying x + 12.5 = 24.233241632 Reorder the terms: 12.5 + x = 24.233241632 Solving 12.5 + x = 24.233241632 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 = 24.233241632 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = 24.233241632 + -12.5 x = 24.233241632 + -12.5 Combine like terms: 24.233241632 + -12.5 = 11.733241632 x = 11.733241632 Simplifying x = 11.733241632Subproblem 2
x + 12.5 = -24.233241632 Simplifying x + 12.5 = -24.233241632 Reorder the terms: 12.5 + x = -24.233241632 Solving 12.5 + x = -24.233241632 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 = -24.233241632 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = -24.233241632 + -12.5 x = -24.233241632 + -12.5 Combine like terms: -24.233241632 + -12.5 = -36.733241632 x = -36.733241632 Simplifying x = -36.733241632Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.733241632, -36.733241632}
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