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Simplifying 2x2 + -45x + -675 = 0 Reorder the terms: -675 + -45x + 2x2 = 0 Solving -675 + -45x + 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'. -337.5 + -22.5x + x2 = 0 Move the constant term to the right: Add '337.5' to each side of the equation. -337.5 + -22.5x + 337.5 + x2 = 0 + 337.5 Reorder the terms: -337.5 + 337.5 + -22.5x + x2 = 0 + 337.5 Combine like terms: -337.5 + 337.5 = 0.0 0.0 + -22.5x + x2 = 0 + 337.5 -22.5x + x2 = 0 + 337.5 Combine like terms: 0 + 337.5 = 337.5 -22.5x + x2 = 337.5 The x term is -22.5x. Take half its coefficient (-11.25). Square it (126.5625) and add it to both sides. Add '126.5625' to each side of the equation. -22.5x + 126.5625 + x2 = 337.5 + 126.5625 Reorder the terms: 126.5625 + -22.5x + x2 = 337.5 + 126.5625 Combine like terms: 337.5 + 126.5625 = 464.0625 126.5625 + -22.5x + x2 = 464.0625 Factor a perfect square on the left side: (x + -11.25)(x + -11.25) = 464.0625 Calculate the square root of the right side: 21.542109925 Break this problem into two subproblems by setting (x + -11.25) equal to 21.542109925 and -21.542109925.Subproblem 1
x + -11.25 = 21.542109925 Simplifying x + -11.25 = 21.542109925 Reorder the terms: -11.25 + x = 21.542109925 Solving -11.25 + x = 21.542109925 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.25' to each side of the equation. -11.25 + 11.25 + x = 21.542109925 + 11.25 Combine like terms: -11.25 + 11.25 = 0.00 0.00 + x = 21.542109925 + 11.25 x = 21.542109925 + 11.25 Combine like terms: 21.542109925 + 11.25 = 32.792109925 x = 32.792109925 Simplifying x = 32.792109925Subproblem 2
x + -11.25 = -21.542109925 Simplifying x + -11.25 = -21.542109925 Reorder the terms: -11.25 + x = -21.542109925 Solving -11.25 + x = -21.542109925 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.25' to each side of the equation. -11.25 + 11.25 + x = -21.542109925 + 11.25 Combine like terms: -11.25 + 11.25 = 0.00 0.00 + x = -21.542109925 + 11.25 x = -21.542109925 + 11.25 Combine like terms: -21.542109925 + 11.25 = -10.292109925 x = -10.292109925 Simplifying x = -10.292109925Solution
The solution to the problem is based on the solutions from the subproblems. x = {32.792109925, -10.292109925}
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