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Simplifying 42x2 + -480x + -2459 = 0 Reorder the terms: -2459 + -480x + 42x2 = 0 Solving -2459 + -480x + 42x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 42 the coefficient of the squared term: Divide each side by '42'. -58.54761905 + -11.42857143x + x2 = 0 Move the constant term to the right: Add '58.54761905' to each side of the equation. -58.54761905 + -11.42857143x + 58.54761905 + x2 = 0 + 58.54761905 Reorder the terms: -58.54761905 + 58.54761905 + -11.42857143x + x2 = 0 + 58.54761905 Combine like terms: -58.54761905 + 58.54761905 = 0.00000000 0.00000000 + -11.42857143x + x2 = 0 + 58.54761905 -11.42857143x + x2 = 0 + 58.54761905 Combine like terms: 0 + 58.54761905 = 58.54761905 -11.42857143x + x2 = 58.54761905 The x term is -11.42857143x. Take half its coefficient (-5.714285715). Square it (32.65306123) and add it to both sides. Add '32.65306123' to each side of the equation. -11.42857143x + 32.65306123 + x2 = 58.54761905 + 32.65306123 Reorder the terms: 32.65306123 + -11.42857143x + x2 = 58.54761905 + 32.65306123 Combine like terms: 58.54761905 + 32.65306123 = 91.20068028 32.65306123 + -11.42857143x + x2 = 91.20068028 Factor a perfect square on the left side: (x + -5.714285715)(x + -5.714285715) = 91.20068028 Calculate the square root of the right side: 9.549904726 Break this problem into two subproblems by setting (x + -5.714285715) equal to 9.549904726 and -9.549904726.Subproblem 1
x + -5.714285715 = 9.549904726 Simplifying x + -5.714285715 = 9.549904726 Reorder the terms: -5.714285715 + x = 9.549904726 Solving -5.714285715 + x = 9.549904726 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.714285715' to each side of the equation. -5.714285715 + 5.714285715 + x = 9.549904726 + 5.714285715 Combine like terms: -5.714285715 + 5.714285715 = 0.000000000 0.000000000 + x = 9.549904726 + 5.714285715 x = 9.549904726 + 5.714285715 Combine like terms: 9.549904726 + 5.714285715 = 15.264190441 x = 15.264190441 Simplifying x = 15.264190441Subproblem 2
x + -5.714285715 = -9.549904726 Simplifying x + -5.714285715 = -9.549904726 Reorder the terms: -5.714285715 + x = -9.549904726 Solving -5.714285715 + x = -9.549904726 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.714285715' to each side of the equation. -5.714285715 + 5.714285715 + x = -9.549904726 + 5.714285715 Combine like terms: -5.714285715 + 5.714285715 = 0.000000000 0.000000000 + x = -9.549904726 + 5.714285715 x = -9.549904726 + 5.714285715 Combine like terms: -9.549904726 + 5.714285715 = -3.835619011 x = -3.835619011 Simplifying x = -3.835619011Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.264190441, -3.835619011}
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