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Simplifying z2 + -4z + -56 = 0 Reorder the terms: -56 + -4z + z2 = 0 Solving -56 + -4z + z2 = 0 Solving for variable 'z'. Begin completing the square. Move the constant term to the right: Add '56' to each side of the equation. -56 + -4z + 56 + z2 = 0 + 56 Reorder the terms: -56 + 56 + -4z + z2 = 0 + 56 Combine like terms: -56 + 56 = 0 0 + -4z + z2 = 0 + 56 -4z + z2 = 0 + 56 Combine like terms: 0 + 56 = 56 -4z + z2 = 56 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 = 56 + 4 Reorder the terms: 4 + -4z + z2 = 56 + 4 Combine like terms: 56 + 4 = 60 4 + -4z + z2 = 60 Factor a perfect square on the left side: (z + -2)(z + -2) = 60 Calculate the square root of the right side: 7.745966692 Break this problem into two subproblems by setting (z + -2) equal to 7.745966692 and -7.745966692.Subproblem 1
z + -2 = 7.745966692 Simplifying z + -2 = 7.745966692 Reorder the terms: -2 + z = 7.745966692 Solving -2 + z = 7.745966692 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 = 7.745966692 + 2 Combine like terms: -2 + 2 = 0 0 + z = 7.745966692 + 2 z = 7.745966692 + 2 Combine like terms: 7.745966692 + 2 = 9.745966692 z = 9.745966692 Simplifying z = 9.745966692Subproblem 2
z + -2 = -7.745966692 Simplifying z + -2 = -7.745966692 Reorder the terms: -2 + z = -7.745966692 Solving -2 + z = -7.745966692 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 = -7.745966692 + 2 Combine like terms: -2 + 2 = 0 0 + z = -7.745966692 + 2 z = -7.745966692 + 2 Combine like terms: -7.745966692 + 2 = -5.745966692 z = -5.745966692 Simplifying z = -5.745966692Solution
The solution to the problem is based on the solutions from the subproblems. z = {9.745966692, -5.745966692}
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