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Simplifying 21x2 + -24x + 2 = 0 Reorder the terms: 2 + -24x + 21x2 = 0 Solving 2 + -24x + 21x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. 0.09523809524 + -1.142857143x + x2 = 0 Move the constant term to the right: Add '-0.09523809524' to each side of the equation. 0.09523809524 + -1.142857143x + -0.09523809524 + x2 = 0 + -0.09523809524 Reorder the terms: 0.09523809524 + -0.09523809524 + -1.142857143x + x2 = 0 + -0.09523809524 Combine like terms: 0.09523809524 + -0.09523809524 = 0.00000000000 0.00000000000 + -1.142857143x + x2 = 0 + -0.09523809524 -1.142857143x + x2 = 0 + -0.09523809524 Combine like terms: 0 + -0.09523809524 = -0.09523809524 -1.142857143x + x2 = -0.09523809524 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 = -0.09523809524 + 0.3265306123 Reorder the terms: 0.3265306123 + -1.142857143x + x2 = -0.09523809524 + 0.3265306123 Combine like terms: -0.09523809524 + 0.3265306123 = 0.23129251706 0.3265306123 + -1.142857143x + x2 = 0.23129251706 Factor a perfect square on the left side: (x + -0.5714285715)(x + -0.5714285715) = 0.23129251706 Calculate the square root of the right side: 0.480928807 Break this problem into two subproblems by setting (x + -0.5714285715) equal to 0.480928807 and -0.480928807.Subproblem 1
x + -0.5714285715 = 0.480928807 Simplifying x + -0.5714285715 = 0.480928807 Reorder the terms: -0.5714285715 + x = 0.480928807 Solving -0.5714285715 + x = 0.480928807 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 = 0.480928807 + 0.5714285715 Combine like terms: -0.5714285715 + 0.5714285715 = 0.0000000000 0.0000000000 + x = 0.480928807 + 0.5714285715 x = 0.480928807 + 0.5714285715 Combine like terms: 0.480928807 + 0.5714285715 = 1.0523573785 x = 1.0523573785 Simplifying x = 1.0523573785Subproblem 2
x + -0.5714285715 = -0.480928807 Simplifying x + -0.5714285715 = -0.480928807 Reorder the terms: -0.5714285715 + x = -0.480928807 Solving -0.5714285715 + x = -0.480928807 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 = -0.480928807 + 0.5714285715 Combine like terms: -0.5714285715 + 0.5714285715 = 0.0000000000 0.0000000000 + x = -0.480928807 + 0.5714285715 x = -0.480928807 + 0.5714285715 Combine like terms: -0.480928807 + 0.5714285715 = 0.0904997645 x = 0.0904997645 Simplifying x = 0.0904997645Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0523573785, 0.0904997645}
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