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Simplifying z2 + -22z + -35 = 0 Reorder the terms: -35 + -22z + z2 = 0 Solving -35 + -22z + 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 + -22z + 35 + z2 = 0 + 35 Reorder the terms: -35 + 35 + -22z + z2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + -22z + z2 = 0 + 35 -22z + z2 = 0 + 35 Combine like terms: 0 + 35 = 35 -22z + z2 = 35 The z term is -22z. Take half its coefficient (-11). Square it (121) and add it to both sides. Add '121' to each side of the equation. -22z + 121 + z2 = 35 + 121 Reorder the terms: 121 + -22z + z2 = 35 + 121 Combine like terms: 35 + 121 = 156 121 + -22z + z2 = 156 Factor a perfect square on the left side: (z + -11)(z + -11) = 156 Calculate the square root of the right side: 12.489995997 Break this problem into two subproblems by setting (z + -11) equal to 12.489995997 and -12.489995997.Subproblem 1
z + -11 = 12.489995997 Simplifying z + -11 = 12.489995997 Reorder the terms: -11 + z = 12.489995997 Solving -11 + z = 12.489995997 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + z = 12.489995997 + 11 Combine like terms: -11 + 11 = 0 0 + z = 12.489995997 + 11 z = 12.489995997 + 11 Combine like terms: 12.489995997 + 11 = 23.489995997 z = 23.489995997 Simplifying z = 23.489995997Subproblem 2
z + -11 = -12.489995997 Simplifying z + -11 = -12.489995997 Reorder the terms: -11 + z = -12.489995997 Solving -11 + z = -12.489995997 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + z = -12.489995997 + 11 Combine like terms: -11 + 11 = 0 0 + z = -12.489995997 + 11 z = -12.489995997 + 11 Combine like terms: -12.489995997 + 11 = -1.489995997 z = -1.489995997 Simplifying z = -1.489995997Solution
The solution to the problem is based on the solutions from the subproblems. z = {23.489995997, -1.489995997}
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