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Simplifying 0.25x2 + -9x + 1 = 0 Reorder the terms: 1 + -9x + 0.25x2 = 0 Solving 1 + -9x + 0.25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.25 the coefficient of the squared term: Divide each side by '0.25'. 4 + -36x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -36x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -36x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -36x + x2 = 0 + -4 -36x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -36x + x2 = -4 The x term is -36x. Take half its coefficient (-18). Square it (324) and add it to both sides. Add '324' to each side of the equation. -36x + 324 + x2 = -4 + 324 Reorder the terms: 324 + -36x + x2 = -4 + 324 Combine like terms: -4 + 324 = 320 324 + -36x + x2 = 320 Factor a perfect square on the left side: (x + -18)(x + -18) = 320 Calculate the square root of the right side: 17.88854382 Break this problem into two subproblems by setting (x + -18) equal to 17.88854382 and -17.88854382.Subproblem 1
x + -18 = 17.88854382 Simplifying x + -18 = 17.88854382 Reorder the terms: -18 + x = 17.88854382 Solving -18 + x = 17.88854382 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + x = 17.88854382 + 18 Combine like terms: -18 + 18 = 0 0 + x = 17.88854382 + 18 x = 17.88854382 + 18 Combine like terms: 17.88854382 + 18 = 35.88854382 x = 35.88854382 Simplifying x = 35.88854382Subproblem 2
x + -18 = -17.88854382 Simplifying x + -18 = -17.88854382 Reorder the terms: -18 + x = -17.88854382 Solving -18 + x = -17.88854382 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + x = -17.88854382 + 18 Combine like terms: -18 + 18 = 0 0 + x = -17.88854382 + 18 x = -17.88854382 + 18 Combine like terms: -17.88854382 + 18 = 0.11145618 x = 0.11145618 Simplifying x = 0.11145618Solution
The solution to the problem is based on the solutions from the subproblems. x = {35.88854382, 0.11145618}
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