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Simplifying 49x2 + -56x + -159 = 0 Reorder the terms: -159 + -56x + 49x2 = 0 Solving -159 + -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'. -3.244897959 + -1.142857143x + x2 = 0 Move the constant term to the right: Add '3.244897959' to each side of the equation. -3.244897959 + -1.142857143x + 3.244897959 + x2 = 0 + 3.244897959 Reorder the terms: -3.244897959 + 3.244897959 + -1.142857143x + x2 = 0 + 3.244897959 Combine like terms: -3.244897959 + 3.244897959 = 0.000000000 0.000000000 + -1.142857143x + x2 = 0 + 3.244897959 -1.142857143x + x2 = 0 + 3.244897959 Combine like terms: 0 + 3.244897959 = 3.244897959 -1.142857143x + x2 = 3.244897959 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 = 3.244897959 + 0.3265306123 Reorder the terms: 0.3265306123 + -1.142857143x + x2 = 3.244897959 + 0.3265306123 Combine like terms: 3.244897959 + 0.3265306123 = 3.5714285713 0.3265306123 + -1.142857143x + x2 = 3.5714285713 Factor a perfect square on the left side: (x + -0.5714285715)(x + -0.5714285715) = 3.5714285713 Calculate the square root of the right side: 1.889822365 Break this problem into two subproblems by setting (x + -0.5714285715) equal to 1.889822365 and -1.889822365.Subproblem 1
x + -0.5714285715 = 1.889822365 Simplifying x + -0.5714285715 = 1.889822365 Reorder the terms: -0.5714285715 + x = 1.889822365 Solving -0.5714285715 + x = 1.889822365 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 = 1.889822365 + 0.5714285715 Combine like terms: -0.5714285715 + 0.5714285715 = 0.0000000000 0.0000000000 + x = 1.889822365 + 0.5714285715 x = 1.889822365 + 0.5714285715 Combine like terms: 1.889822365 + 0.5714285715 = 2.4612509365 x = 2.4612509365 Simplifying x = 2.4612509365Subproblem 2
x + -0.5714285715 = -1.889822365 Simplifying x + -0.5714285715 = -1.889822365 Reorder the terms: -0.5714285715 + x = -1.889822365 Solving -0.5714285715 + x = -1.889822365 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 = -1.889822365 + 0.5714285715 Combine like terms: -0.5714285715 + 0.5714285715 = 0.0000000000 0.0000000000 + x = -1.889822365 + 0.5714285715 x = -1.889822365 + 0.5714285715 Combine like terms: -1.889822365 + 0.5714285715 = -1.3183937935 x = -1.3183937935 Simplifying x = -1.3183937935Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.4612509365, -1.3183937935}
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