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Simplifying 49x2 + 168x + -60 = 0 Reorder the terms: -60 + 168x + 49x2 = 0 Solving -60 + 168x + 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'. -1.224489796 + 3.428571429x + x2 = 0 Move the constant term to the right: Add '1.224489796' to each side of the equation. -1.224489796 + 3.428571429x + 1.224489796 + x2 = 0 + 1.224489796 Reorder the terms: -1.224489796 + 1.224489796 + 3.428571429x + x2 = 0 + 1.224489796 Combine like terms: -1.224489796 + 1.224489796 = 0.000000000 0.000000000 + 3.428571429x + x2 = 0 + 1.224489796 3.428571429x + x2 = 0 + 1.224489796 Combine like terms: 0 + 1.224489796 = 1.224489796 3.428571429x + x2 = 1.224489796 The x term is 3.428571429x. Take half its coefficient (1.714285715). Square it (2.938775513) and add it to both sides. Add '2.938775513' to each side of the equation. 3.428571429x + 2.938775513 + x2 = 1.224489796 + 2.938775513 Reorder the terms: 2.938775513 + 3.428571429x + x2 = 1.224489796 + 2.938775513 Combine like terms: 1.224489796 + 2.938775513 = 4.163265309 2.938775513 + 3.428571429x + x2 = 4.163265309 Factor a perfect square on the left side: (x + 1.714285715)(x + 1.714285715) = 4.163265309 Calculate the square root of the right side: 2.040408123 Break this problem into two subproblems by setting (x + 1.714285715) equal to 2.040408123 and -2.040408123.Subproblem 1
x + 1.714285715 = 2.040408123 Simplifying x + 1.714285715 = 2.040408123 Reorder the terms: 1.714285715 + x = 2.040408123 Solving 1.714285715 + x = 2.040408123 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.714285715' to each side of the equation. 1.714285715 + -1.714285715 + x = 2.040408123 + -1.714285715 Combine like terms: 1.714285715 + -1.714285715 = 0.000000000 0.000000000 + x = 2.040408123 + -1.714285715 x = 2.040408123 + -1.714285715 Combine like terms: 2.040408123 + -1.714285715 = 0.326122408 x = 0.326122408 Simplifying x = 0.326122408Subproblem 2
x + 1.714285715 = -2.040408123 Simplifying x + 1.714285715 = -2.040408123 Reorder the terms: 1.714285715 + x = -2.040408123 Solving 1.714285715 + x = -2.040408123 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.714285715' to each side of the equation. 1.714285715 + -1.714285715 + x = -2.040408123 + -1.714285715 Combine like terms: 1.714285715 + -1.714285715 = 0.000000000 0.000000000 + x = -2.040408123 + -1.714285715 x = -2.040408123 + -1.714285715 Combine like terms: -2.040408123 + -1.714285715 = -3.754693838 x = -3.754693838 Simplifying x = -3.754693838Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.326122408, -3.754693838}
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