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Simplifying 49(3.14) * x2 + -56(3.14) * x + 16(3.14) = 0 Multiply 49 * 3.14 153.86x2 + -56(3.14) * x + 16(3.14) = 0 Multiply -56 * 3.14 153.86x2 + -175.84x + 16(3.14) = 0 Multiply 16 * 3.14 153.86x2 + -175.84x + 50.24 = 0 Reorder the terms: 50.24 + -175.84x + 153.86x2 = 0 Solving 50.24 + -175.84x + 153.86x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 153.86 the coefficient of the squared term: Divide each side by '153.86'. 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 = 0.0000000001 0.3265306123 + -1.142857143x + x2 = 0.0000000001 Factor a perfect square on the left side: (x + -0.5714285715)(x + -0.5714285715) = 0.0000000001 Calculate the square root of the right side: 0.00001 Break this problem into two subproblems by setting (x + -0.5714285715) equal to 0.00001 and -0.00001.Subproblem 1
x + -0.5714285715 = 0.00001 Simplifying x + -0.5714285715 = 0.00001 Reorder the terms: -0.5714285715 + x = 0.00001 Solving -0.5714285715 + x = 0.00001 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 = 0.00001 + 0.5714285715 Combine like terms: -0.5714285715 + 0.5714285715 = 0.0000000000 0.0000000000 + x = 0.00001 + 0.5714285715 x = 0.00001 + 0.5714285715 Combine like terms: 0.00001 + 0.5714285715 = 0.5714385715 x = 0.5714385715 Simplifying x = 0.5714385715Subproblem 2
x + -0.5714285715 = -0.00001 Simplifying x + -0.5714285715 = -0.00001 Reorder the terms: -0.5714285715 + x = -0.00001 Solving -0.5714285715 + x = -0.00001 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 = -0.00001 + 0.5714285715 Combine like terms: -0.5714285715 + 0.5714285715 = 0.0000000000 0.0000000000 + x = -0.00001 + 0.5714285715 x = -0.00001 + 0.5714285715 Combine like terms: -0.00001 + 0.5714285715 = 0.5714185715 x = 0.5714185715 Simplifying x = 0.5714185715Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5714385715, 0.5714185715}
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