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Simplifying 49x2 = 56x + 16 Reorder the terms: 49x2 = 16 + 56x Solving 49x2 = 16 + 56x Solving for variable 'x'. Reorder the terms: -16 + -56x + 49x2 = 16 + 56x + -16 + -56x Reorder the terms: -16 + -56x + 49x2 = 16 + -16 + 56x + -56x Combine like terms: 16 + -16 = 0 -16 + -56x + 49x2 = 0 + 56x + -56x -16 + -56x + 49x2 = 56x + -56x Combine like terms: 56x + -56x = 0 -16 + -56x + 49x2 = 0 Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. -0.3265306122 + -1.142857143x + x2 = 0 Move the constant term to the right: Add '0.3265306122' to each side of the equation. -0.3265306122 + -1.142857143x + 0.3265306122 + x2 = 0 + 0.3265306122 Reorder the terms: -0.3265306122 + 0.3265306122 + -1.142857143x + x2 = 0 + 0.3265306122 Combine like terms: -0.3265306122 + 0.3265306122 = 0.0000000000 0.0000000000 + -1.142857143x + x2 = 0 + 0.3265306122 -1.142857143x + x2 = 0 + 0.3265306122 Combine like terms: 0 + 0.3265306122 = 0.3265306122 -1.142857143x + x2 = 0.3265306122 The x term is -1.142857143x. Take half its coefficient (-0.5714285715). Square it (0.3265306123) and add it to both sides. Add '0.3265306123' to each side of the equation. -1.142857143x + 0.3265306123 + x2 = 0.3265306122 + 0.3265306123 Reorder the terms: 0.3265306123 + -1.142857143x + x2 = 0.3265306122 + 0.3265306123 Combine like terms: 0.3265306122 + 0.3265306123 = 0.6530612245 0.3265306123 + -1.142857143x + x2 = 0.6530612245 Factor a perfect square on the left side: (x + -0.5714285715)(x + -0.5714285715) = 0.6530612245 Calculate the square root of the right side: 0.808122036 Break this problem into two subproblems by setting (x + -0.5714285715) equal to 0.808122036 and -0.808122036.Subproblem 1
x + -0.5714285715 = 0.808122036 Simplifying x + -0.5714285715 = 0.808122036 Reorder the terms: -0.5714285715 + x = 0.808122036 Solving -0.5714285715 + x = 0.808122036 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5714285715' to each side of the equation. -0.5714285715 + 0.5714285715 + x = 0.808122036 + 0.5714285715 Combine like terms: -0.5714285715 + 0.5714285715 = 0.0000000000 0.0000000000 + x = 0.808122036 + 0.5714285715 x = 0.808122036 + 0.5714285715 Combine like terms: 0.808122036 + 0.5714285715 = 1.3795506075 x = 1.3795506075 Simplifying x = 1.3795506075Subproblem 2
x + -0.5714285715 = -0.808122036 Simplifying x + -0.5714285715 = -0.808122036 Reorder the terms: -0.5714285715 + x = -0.808122036 Solving -0.5714285715 + x = -0.808122036 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5714285715' to each side of the equation. -0.5714285715 + 0.5714285715 + x = -0.808122036 + 0.5714285715 Combine like terms: -0.5714285715 + 0.5714285715 = 0.0000000000 0.0000000000 + x = -0.808122036 + 0.5714285715 x = -0.808122036 + 0.5714285715 Combine like terms: -0.808122036 + 0.5714285715 = -0.2366934645 x = -0.2366934645 Simplifying x = -0.2366934645Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.3795506075, -0.2366934645}
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