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Simplifying 2z2 + -21z + -336 = 0 Reorder the terms: -336 + -21z + 2z2 = 0 Solving -336 + -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'. -168 + -10.5z + z2 = 0 Move the constant term to the right: Add '168' to each side of the equation. -168 + -10.5z + 168 + z2 = 0 + 168 Reorder the terms: -168 + 168 + -10.5z + z2 = 0 + 168 Combine like terms: -168 + 168 = 0 0 + -10.5z + z2 = 0 + 168 -10.5z + z2 = 0 + 168 Combine like terms: 0 + 168 = 168 -10.5z + z2 = 168 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 = 168 + 27.5625 Reorder the terms: 27.5625 + -10.5z + z2 = 168 + 27.5625 Combine like terms: 168 + 27.5625 = 195.5625 27.5625 + -10.5z + z2 = 195.5625 Factor a perfect square on the left side: (z + -5.25)(z + -5.25) = 195.5625 Calculate the square root of the right side: 13.984366271 Break this problem into two subproblems by setting (z + -5.25) equal to 13.984366271 and -13.984366271.Subproblem 1
z + -5.25 = 13.984366271 Simplifying z + -5.25 = 13.984366271 Reorder the terms: -5.25 + z = 13.984366271 Solving -5.25 + z = 13.984366271 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 = 13.984366271 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + z = 13.984366271 + 5.25 z = 13.984366271 + 5.25 Combine like terms: 13.984366271 + 5.25 = 19.234366271 z = 19.234366271 Simplifying z = 19.234366271Subproblem 2
z + -5.25 = -13.984366271 Simplifying z + -5.25 = -13.984366271 Reorder the terms: -5.25 + z = -13.984366271 Solving -5.25 + z = -13.984366271 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 = -13.984366271 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + z = -13.984366271 + 5.25 z = -13.984366271 + 5.25 Combine like terms: -13.984366271 + 5.25 = -8.734366271 z = -8.734366271 Simplifying z = -8.734366271Solution
The solution to the problem is based on the solutions from the subproblems. z = {19.234366271, -8.734366271}
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