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Simplifying 7z2 + -8z + 2 = 0 Reorder the terms: 2 + -8z + 7z2 = 0 Solving 2 + -8z + 7z2 = 0 Solving for variable 'z'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.2857142857 + -1.142857143z + z2 = 0 Move the constant term to the right: Add '-0.2857142857' to each side of the equation. 0.2857142857 + -1.142857143z + -0.2857142857 + z2 = 0 + -0.2857142857 Reorder the terms: 0.2857142857 + -0.2857142857 + -1.142857143z + z2 = 0 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + -1.142857143z + z2 = 0 + -0.2857142857 -1.142857143z + z2 = 0 + -0.2857142857 Combine like terms: 0 + -0.2857142857 = -0.2857142857 -1.142857143z + z2 = -0.2857142857 The z term is -1.142857143z. 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. -1.142857143z + 0.3265306123 + z2 = -0.2857142857 + 0.3265306123 Reorder the terms: 0.3265306123 + -1.142857143z + z2 = -0.2857142857 + 0.3265306123 Combine like terms: -0.2857142857 + 0.3265306123 = 0.0408163266 0.3265306123 + -1.142857143z + z2 = 0.0408163266 Factor a perfect square on the left side: (z + -0.5714285715)(z + -0.5714285715) = 0.0408163266 Calculate the square root of the right side: 0.202030509 Break this problem into two subproblems by setting (z + -0.5714285715) equal to 0.202030509 and -0.202030509.Subproblem 1
z + -0.5714285715 = 0.202030509 Simplifying z + -0.5714285715 = 0.202030509 Reorder the terms: -0.5714285715 + z = 0.202030509 Solving -0.5714285715 + z = 0.202030509 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '0.5714285715' to each side of the equation. -0.5714285715 + 0.5714285715 + z = 0.202030509 + 0.5714285715 Combine like terms: -0.5714285715 + 0.5714285715 = 0.0000000000 0.0000000000 + z = 0.202030509 + 0.5714285715 z = 0.202030509 + 0.5714285715 Combine like terms: 0.202030509 + 0.5714285715 = 0.7734590805 z = 0.7734590805 Simplifying z = 0.7734590805Subproblem 2
z + -0.5714285715 = -0.202030509 Simplifying z + -0.5714285715 = -0.202030509 Reorder the terms: -0.5714285715 + z = -0.202030509 Solving -0.5714285715 + z = -0.202030509 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '0.5714285715' to each side of the equation. -0.5714285715 + 0.5714285715 + z = -0.202030509 + 0.5714285715 Combine like terms: -0.5714285715 + 0.5714285715 = 0.0000000000 0.0000000000 + z = -0.202030509 + 0.5714285715 z = -0.202030509 + 0.5714285715 Combine like terms: -0.202030509 + 0.5714285715 = 0.3693980625 z = 0.3693980625 Simplifying z = 0.3693980625Solution
The solution to the problem is based on the solutions from the subproblems. z = {0.7734590805, 0.3693980625}
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