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Simplifying 4x2 + 23x + 25 = 0 Reorder the terms: 25 + 23x + 4x2 = 0 Solving 25 + 23x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 6.25 + 5.75x + x2 = 0 Move the constant term to the right: Add '-6.25' to each side of the equation. 6.25 + 5.75x + -6.25 + x2 = 0 + -6.25 Reorder the terms: 6.25 + -6.25 + 5.75x + x2 = 0 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + 5.75x + x2 = 0 + -6.25 5.75x + x2 = 0 + -6.25 Combine like terms: 0 + -6.25 = -6.25 5.75x + x2 = -6.25 The x term is 5.75x. Take half its coefficient (2.875). Square it (8.265625) and add it to both sides. Add '8.265625' to each side of the equation. 5.75x + 8.265625 + x2 = -6.25 + 8.265625 Reorder the terms: 8.265625 + 5.75x + x2 = -6.25 + 8.265625 Combine like terms: -6.25 + 8.265625 = 2.015625 8.265625 + 5.75x + x2 = 2.015625 Factor a perfect square on the left side: (x + 2.875)(x + 2.875) = 2.015625 Calculate the square root of the right side: 1.419727086 Break this problem into two subproblems by setting (x + 2.875) equal to 1.419727086 and -1.419727086.Subproblem 1
x + 2.875 = 1.419727086 Simplifying x + 2.875 = 1.419727086 Reorder the terms: 2.875 + x = 1.419727086 Solving 2.875 + x = 1.419727086 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.875' to each side of the equation. 2.875 + -2.875 + x = 1.419727086 + -2.875 Combine like terms: 2.875 + -2.875 = 0.000 0.000 + x = 1.419727086 + -2.875 x = 1.419727086 + -2.875 Combine like terms: 1.419727086 + -2.875 = -1.455272914 x = -1.455272914 Simplifying x = -1.455272914Subproblem 2
x + 2.875 = -1.419727086 Simplifying x + 2.875 = -1.419727086 Reorder the terms: 2.875 + x = -1.419727086 Solving 2.875 + x = -1.419727086 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.875' to each side of the equation. 2.875 + -2.875 + x = -1.419727086 + -2.875 Combine like terms: 2.875 + -2.875 = 0.000 0.000 + x = -1.419727086 + -2.875 x = -1.419727086 + -2.875 Combine like terms: -1.419727086 + -2.875 = -4.294727086 x = -4.294727086 Simplifying x = -4.294727086Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.455272914, -4.294727086}
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