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Simplifying 2x2 + 45x + -719 = 0 Reorder the terms: -719 + 45x + 2x2 = 0 Solving -719 + 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'. -359.5 + 22.5x + x2 = 0 Move the constant term to the right: Add '359.5' to each side of the equation. -359.5 + 22.5x + 359.5 + x2 = 0 + 359.5 Reorder the terms: -359.5 + 359.5 + 22.5x + x2 = 0 + 359.5 Combine like terms: -359.5 + 359.5 = 0.0 0.0 + 22.5x + x2 = 0 + 359.5 22.5x + x2 = 0 + 359.5 Combine like terms: 0 + 359.5 = 359.5 22.5x + x2 = 359.5 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 = 359.5 + 126.5625 Reorder the terms: 126.5625 + 22.5x + x2 = 359.5 + 126.5625 Combine like terms: 359.5 + 126.5625 = 486.0625 126.5625 + 22.5x + x2 = 486.0625 Factor a perfect square on the left side: (x + 11.25)(x + 11.25) = 486.0625 Calculate the square root of the right side: 22.046825168 Break this problem into two subproblems by setting (x + 11.25) equal to 22.046825168 and -22.046825168.Subproblem 1
x + 11.25 = 22.046825168 Simplifying x + 11.25 = 22.046825168 Reorder the terms: 11.25 + x = 22.046825168 Solving 11.25 + x = 22.046825168 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 = 22.046825168 + -11.25 Combine like terms: 11.25 + -11.25 = 0.00 0.00 + x = 22.046825168 + -11.25 x = 22.046825168 + -11.25 Combine like terms: 22.046825168 + -11.25 = 10.796825168 x = 10.796825168 Simplifying x = 10.796825168Subproblem 2
x + 11.25 = -22.046825168 Simplifying x + 11.25 = -22.046825168 Reorder the terms: 11.25 + x = -22.046825168 Solving 11.25 + x = -22.046825168 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 = -22.046825168 + -11.25 Combine like terms: 11.25 + -11.25 = 0.00 0.00 + x = -22.046825168 + -11.25 x = -22.046825168 + -11.25 Combine like terms: -22.046825168 + -11.25 = -33.296825168 x = -33.296825168 Simplifying x = -33.296825168Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.796825168, -33.296825168}
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