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Simplifying 2z2 + -21z + 50 = 0 Reorder the terms: 50 + -21z + 2z2 = 0 Solving 50 + -21z + 2z2 = 0 Solving for variable 'z'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 25 + -10.5z + z2 = 0 Move the constant term to the right: Add '-25' to each side of the equation. 25 + -10.5z + -25 + z2 = 0 + -25 Reorder the terms: 25 + -25 + -10.5z + z2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -10.5z + z2 = 0 + -25 -10.5z + z2 = 0 + -25 Combine like terms: 0 + -25 = -25 -10.5z + z2 = -25 The z term is -10.5z. Take half its coefficient (-5.25). Square it (27.5625) and add it to both sides. Add '27.5625' to each side of the equation. -10.5z + 27.5625 + z2 = -25 + 27.5625 Reorder the terms: 27.5625 + -10.5z + z2 = -25 + 27.5625 Combine like terms: -25 + 27.5625 = 2.5625 27.5625 + -10.5z + z2 = 2.5625 Factor a perfect square on the left side: (z + -5.25)(z + -5.25) = 2.5625 Calculate the square root of the right side: 1.600781059 Break this problem into two subproblems by setting (z + -5.25) equal to 1.600781059 and -1.600781059.Subproblem 1
z + -5.25 = 1.600781059 Simplifying z + -5.25 = 1.600781059 Reorder the terms: -5.25 + z = 1.600781059 Solving -5.25 + z = 1.600781059 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '5.25' to each side of the equation. -5.25 + 5.25 + z = 1.600781059 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + z = 1.600781059 + 5.25 z = 1.600781059 + 5.25 Combine like terms: 1.600781059 + 5.25 = 6.850781059 z = 6.850781059 Simplifying z = 6.850781059Subproblem 2
z + -5.25 = -1.600781059 Simplifying z + -5.25 = -1.600781059 Reorder the terms: -5.25 + z = -1.600781059 Solving -5.25 + z = -1.600781059 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '5.25' to each side of the equation. -5.25 + 5.25 + z = -1.600781059 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + z = -1.600781059 + 5.25 z = -1.600781059 + 5.25 Combine like terms: -1.600781059 + 5.25 = 3.649218941 z = 3.649218941 Simplifying z = 3.649218941Solution
The solution to the problem is based on the solutions from the subproblems. z = {6.850781059, 3.649218941}
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