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Simplifying (49x2) + -56x + 10 = 0 Reorder the terms: 10 + -56x + (49x2) = 0 Solving 10 + -56x + (49x2) = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. 0.2040816327 + -1.142857143x + x2 = 0 Move the constant term to the right: Add '-0.2040816327' to each side of the equation. 0.2040816327 + -1.142857143x + -0.2040816327 + x2 = 0 + -0.2040816327 Reorder the terms: 0.2040816327 + -0.2040816327 + -1.142857143x + x2 = 0 + -0.2040816327 Combine like terms: 0.2040816327 + -0.2040816327 = 0.0000000000 0.0000000000 + -1.142857143x + x2 = 0 + -0.2040816327 -1.142857143x + x2 = 0 + -0.2040816327 Combine like terms: 0 + -0.2040816327 = -0.2040816327 -1.142857143x + x2 = -0.2040816327 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 = -0.2040816327 + 0.3265306123 Reorder the terms: 0.3265306123 + -1.142857143x + x2 = -0.2040816327 + 0.3265306123 Combine like terms: -0.2040816327 + 0.3265306123 = 0.1224489796 0.3265306123 + -1.142857143x + x2 = 0.1224489796 Factor a perfect square on the left side: ((x) + -0.5714285715)((x) + -0.5714285715) = 0.1224489796 Calculate the square root of the right side: 0.349927106 Break this problem into two subproblems by setting ((x) + -0.5714285715) equal to 0.349927106 and -0.349927106.Subproblem 1
(x) + -0.5714285715 = 0.349927106 Simplifying (x) + -0.5714285715 = 0.349927106 x + -0.5714285715 = 0.349927106 Reorder the terms: -0.5714285715 + x = 0.349927106 Solving -0.5714285715 + x = 0.349927106 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 = 0.349927106 + 0.5714285715 Combine like terms: -0.5714285715 + 0.5714285715 = 0.0000000000 0.0000000000 + x = 0.349927106 + 0.5714285715 x = 0.349927106 + 0.5714285715 Combine like terms: 0.349927106 + 0.5714285715 = 0.9213556775 x = 0.9213556775 Simplifying x = 0.9213556775Subproblem 2
(x) + -0.5714285715 = -0.349927106 Simplifying (x) + -0.5714285715 = -0.349927106 x + -0.5714285715 = -0.349927106 Reorder the terms: -0.5714285715 + x = -0.349927106 Solving -0.5714285715 + x = -0.349927106 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 = -0.349927106 + 0.5714285715 Combine like terms: -0.5714285715 + 0.5714285715 = 0.0000000000 0.0000000000 + x = -0.349927106 + 0.5714285715 x = -0.349927106 + 0.5714285715 Combine like terms: -0.349927106 + 0.5714285715 = 0.2215014655 x = 0.2215014655 Simplifying x = 0.2215014655Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9213556775, 0.2215014655}
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