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Simplifying 2x2 + -45x + -60 = 0 Reorder the terms: -60 + -45x + 2x2 = 0 Solving -60 + -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'. -30 + -22.5x + x2 = 0 Move the constant term to the right: Add '30' to each side of the equation. -30 + -22.5x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + -22.5x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + -22.5x + x2 = 0 + 30 -22.5x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 -22.5x + x2 = 30 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 = 30 + 126.5625 Reorder the terms: 126.5625 + -22.5x + x2 = 30 + 126.5625 Combine like terms: 30 + 126.5625 = 156.5625 126.5625 + -22.5x + x2 = 156.5625 Factor a perfect square on the left side: (x + -11.25)(x + -11.25) = 156.5625 Calculate the square root of the right side: 12.512493756 Break this problem into two subproblems by setting (x + -11.25) equal to 12.512493756 and -12.512493756.Subproblem 1
x + -11.25 = 12.512493756 Simplifying x + -11.25 = 12.512493756 Reorder the terms: -11.25 + x = 12.512493756 Solving -11.25 + x = 12.512493756 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 = 12.512493756 + 11.25 Combine like terms: -11.25 + 11.25 = 0.00 0.00 + x = 12.512493756 + 11.25 x = 12.512493756 + 11.25 Combine like terms: 12.512493756 + 11.25 = 23.762493756 x = 23.762493756 Simplifying x = 23.762493756Subproblem 2
x + -11.25 = -12.512493756 Simplifying x + -11.25 = -12.512493756 Reorder the terms: -11.25 + x = -12.512493756 Solving -11.25 + x = -12.512493756 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 = -12.512493756 + 11.25 Combine like terms: -11.25 + 11.25 = 0.00 0.00 + x = -12.512493756 + 11.25 x = -12.512493756 + 11.25 Combine like terms: -12.512493756 + 11.25 = -1.262493756 x = -1.262493756 Simplifying x = -1.262493756Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.762493756, -1.262493756}
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