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Simplifying 2x2 + -46x + 57 = 0 Reorder the terms: 57 + -46x + 2x2 = 0 Solving 57 + -46x + 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'. 28.5 + -23x + x2 = 0 Move the constant term to the right: Add '-28.5' to each side of the equation. 28.5 + -23x + -28.5 + x2 = 0 + -28.5 Reorder the terms: 28.5 + -28.5 + -23x + x2 = 0 + -28.5 Combine like terms: 28.5 + -28.5 = 0.0 0.0 + -23x + x2 = 0 + -28.5 -23x + x2 = 0 + -28.5 Combine like terms: 0 + -28.5 = -28.5 -23x + x2 = -28.5 The x term is -23x. Take half its coefficient (-11.5). Square it (132.25) and add it to both sides. Add '132.25' to each side of the equation. -23x + 132.25 + x2 = -28.5 + 132.25 Reorder the terms: 132.25 + -23x + x2 = -28.5 + 132.25 Combine like terms: -28.5 + 132.25 = 103.75 132.25 + -23x + x2 = 103.75 Factor a perfect square on the left side: (x + -11.5)(x + -11.5) = 103.75 Calculate the square root of the right side: 10.185774394 Break this problem into two subproblems by setting (x + -11.5) equal to 10.185774394 and -10.185774394.Subproblem 1
x + -11.5 = 10.185774394 Simplifying x + -11.5 = 10.185774394 Reorder the terms: -11.5 + x = 10.185774394 Solving -11.5 + x = 10.185774394 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + x = 10.185774394 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = 10.185774394 + 11.5 x = 10.185774394 + 11.5 Combine like terms: 10.185774394 + 11.5 = 21.685774394 x = 21.685774394 Simplifying x = 21.685774394Subproblem 2
x + -11.5 = -10.185774394 Simplifying x + -11.5 = -10.185774394 Reorder the terms: -11.5 + x = -10.185774394 Solving -11.5 + x = -10.185774394 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + x = -10.185774394 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = -10.185774394 + 11.5 x = -10.185774394 + 11.5 Combine like terms: -10.185774394 + 11.5 = 1.314225606 x = 1.314225606 Simplifying x = 1.314225606Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.685774394, 1.314225606}
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