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Simplifying 2x2 + -25x + -54 = 0 Reorder the terms: -54 + -25x + 2x2 = 0 Solving -54 + -25x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -27 + -12.5x + x2 = 0 Move the constant term to the right: Add '27' to each side of the equation. -27 + -12.5x + 27 + x2 = 0 + 27 Reorder the terms: -27 + 27 + -12.5x + x2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + -12.5x + x2 = 0 + 27 -12.5x + x2 = 0 + 27 Combine like terms: 0 + 27 = 27 -12.5x + x2 = 27 The x term is -12.5x. Take half its coefficient (-6.25). Square it (39.0625) and add it to both sides. Add '39.0625' to each side of the equation. -12.5x + 39.0625 + x2 = 27 + 39.0625 Reorder the terms: 39.0625 + -12.5x + x2 = 27 + 39.0625 Combine like terms: 27 + 39.0625 = 66.0625 39.0625 + -12.5x + x2 = 66.0625 Factor a perfect square on the left side: (x + -6.25)(x + -6.25) = 66.0625 Calculate the square root of the right side: 8.127884104 Break this problem into two subproblems by setting (x + -6.25) equal to 8.127884104 and -8.127884104.Subproblem 1
x + -6.25 = 8.127884104 Simplifying x + -6.25 = 8.127884104 Reorder the terms: -6.25 + x = 8.127884104 Solving -6.25 + x = 8.127884104 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + x = 8.127884104 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = 8.127884104 + 6.25 x = 8.127884104 + 6.25 Combine like terms: 8.127884104 + 6.25 = 14.377884104 x = 14.377884104 Simplifying x = 14.377884104Subproblem 2
x + -6.25 = -8.127884104 Simplifying x + -6.25 = -8.127884104 Reorder the terms: -6.25 + x = -8.127884104 Solving -6.25 + x = -8.127884104 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + x = -8.127884104 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = -8.127884104 + 6.25 x = -8.127884104 + 6.25 Combine like terms: -8.127884104 + 6.25 = -1.877884104 x = -1.877884104 Simplifying x = -1.877884104Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.377884104, -1.877884104}
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