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Simplifying 2x2 + -45x + -91 = 0 Reorder the terms: -91 + -45x + 2x2 = 0 Solving -91 + -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'. -45.5 + -22.5x + x2 = 0 Move the constant term to the right: Add '45.5' to each side of the equation. -45.5 + -22.5x + 45.5 + x2 = 0 + 45.5 Reorder the terms: -45.5 + 45.5 + -22.5x + x2 = 0 + 45.5 Combine like terms: -45.5 + 45.5 = 0.0 0.0 + -22.5x + x2 = 0 + 45.5 -22.5x + x2 = 0 + 45.5 Combine like terms: 0 + 45.5 = 45.5 -22.5x + x2 = 45.5 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 = 45.5 + 126.5625 Reorder the terms: 126.5625 + -22.5x + x2 = 45.5 + 126.5625 Combine like terms: 45.5 + 126.5625 = 172.0625 126.5625 + -22.5x + x2 = 172.0625 Factor a perfect square on the left side: (x + -11.25)(x + -11.25) = 172.0625 Calculate the square root of the right side: 13.117259622 Break this problem into two subproblems by setting (x + -11.25) equal to 13.117259622 and -13.117259622.Subproblem 1
x + -11.25 = 13.117259622 Simplifying x + -11.25 = 13.117259622 Reorder the terms: -11.25 + x = 13.117259622 Solving -11.25 + x = 13.117259622 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 = 13.117259622 + 11.25 Combine like terms: -11.25 + 11.25 = 0.00 0.00 + x = 13.117259622 + 11.25 x = 13.117259622 + 11.25 Combine like terms: 13.117259622 + 11.25 = 24.367259622 x = 24.367259622 Simplifying x = 24.367259622Subproblem 2
x + -11.25 = -13.117259622 Simplifying x + -11.25 = -13.117259622 Reorder the terms: -11.25 + x = -13.117259622 Solving -11.25 + x = -13.117259622 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 = -13.117259622 + 11.25 Combine like terms: -11.25 + 11.25 = 0.00 0.00 + x = -13.117259622 + 11.25 x = -13.117259622 + 11.25 Combine like terms: -13.117259622 + 11.25 = -1.867259622 x = -1.867259622 Simplifying x = -1.867259622Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.367259622, -1.867259622}
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