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Simplifying z2 + -4z + -35 = 0 Reorder the terms: -35 + -4z + z2 = 0 Solving -35 + -4z + z2 = 0 Solving for variable 'z'. Begin completing the square. Move the constant term to the right: Add '35' to each side of the equation. -35 + -4z + 35 + z2 = 0 + 35 Reorder the terms: -35 + 35 + -4z + z2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + -4z + z2 = 0 + 35 -4z + z2 = 0 + 35 Combine like terms: 0 + 35 = 35 -4z + z2 = 35 The z term is -4z. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4z + 4 + z2 = 35 + 4 Reorder the terms: 4 + -4z + z2 = 35 + 4 Combine like terms: 35 + 4 = 39 4 + -4z + z2 = 39 Factor a perfect square on the left side: (z + -2)(z + -2) = 39 Calculate the square root of the right side: 6.244997998 Break this problem into two subproblems by setting (z + -2) equal to 6.244997998 and -6.244997998.Subproblem 1
z + -2 = 6.244997998 Simplifying z + -2 = 6.244997998 Reorder the terms: -2 + z = 6.244997998 Solving -2 + z = 6.244997998 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + z = 6.244997998 + 2 Combine like terms: -2 + 2 = 0 0 + z = 6.244997998 + 2 z = 6.244997998 + 2 Combine like terms: 6.244997998 + 2 = 8.244997998 z = 8.244997998 Simplifying z = 8.244997998Subproblem 2
z + -2 = -6.244997998 Simplifying z + -2 = -6.244997998 Reorder the terms: -2 + z = -6.244997998 Solving -2 + z = -6.244997998 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + z = -6.244997998 + 2 Combine like terms: -2 + 2 = 0 0 + z = -6.244997998 + 2 z = -6.244997998 + 2 Combine like terms: -6.244997998 + 2 = -4.244997998 z = -4.244997998 Simplifying z = -4.244997998Solution
The solution to the problem is based on the solutions from the subproblems. z = {8.244997998, -4.244997998}
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