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Simplifying 2x2 + -45x + -252 = 0 Reorder the terms: -252 + -45x + 2x2 = 0 Solving -252 + -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'. -126 + -22.5x + x2 = 0 Move the constant term to the right: Add '126' to each side of the equation. -126 + -22.5x + 126 + x2 = 0 + 126 Reorder the terms: -126 + 126 + -22.5x + x2 = 0 + 126 Combine like terms: -126 + 126 = 0 0 + -22.5x + x2 = 0 + 126 -22.5x + x2 = 0 + 126 Combine like terms: 0 + 126 = 126 -22.5x + x2 = 126 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 = 126 + 126.5625 Reorder the terms: 126.5625 + -22.5x + x2 = 126 + 126.5625 Combine like terms: 126 + 126.5625 = 252.5625 126.5625 + -22.5x + x2 = 252.5625 Factor a perfect square on the left side: (x + -11.25)(x + -11.25) = 252.5625 Calculate the square root of the right side: 15.892215075 Break this problem into two subproblems by setting (x + -11.25) equal to 15.892215075 and -15.892215075.Subproblem 1
x + -11.25 = 15.892215075 Simplifying x + -11.25 = 15.892215075 Reorder the terms: -11.25 + x = 15.892215075 Solving -11.25 + x = 15.892215075 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 = 15.892215075 + 11.25 Combine like terms: -11.25 + 11.25 = 0.00 0.00 + x = 15.892215075 + 11.25 x = 15.892215075 + 11.25 Combine like terms: 15.892215075 + 11.25 = 27.142215075 x = 27.142215075 Simplifying x = 27.142215075Subproblem 2
x + -11.25 = -15.892215075 Simplifying x + -11.25 = -15.892215075 Reorder the terms: -11.25 + x = -15.892215075 Solving -11.25 + x = -15.892215075 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 = -15.892215075 + 11.25 Combine like terms: -11.25 + 11.25 = 0.00 0.00 + x = -15.892215075 + 11.25 x = -15.892215075 + 11.25 Combine like terms: -15.892215075 + 11.25 = -4.642215075 x = -4.642215075 Simplifying x = -4.642215075Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.142215075, -4.642215075}
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