5-z=1-(z+1)(z-1)

Solution for 5-z=1-(z+1)(z-1) equation:

Simplifying
5 + -1z = 1 + -1(z + 1)(z + -1)

Reorder the terms:
5 + -1z = 1 + -1(1 + z)(z + -1)

Reorder the terms:
5 + -1z = 1 + -1(1 + z)(-1 + z)

Multiply (1 + z) * (-1 + z)
5 + -1z = 1 + -1(1(-1 + z) + z(-1 + z))
5 + -1z = 1 + -1((-1 * 1 + z * 1) + z(-1 + z))
5 + -1z = 1 + -1((-1 + 1z) + z(-1 + z))
5 + -1z = 1 + -1(-1 + 1z + (-1 * z + z * z))
5 + -1z = 1 + -1(-1 + 1z + (-1z + z2))

Combine like terms: 1z + -1z = 0
5 + -1z = 1 + -1(-1 + 0 + z2)
5 + -1z = 1 + -1(-1 + z2)
5 + -1z = 1 + (-1 * -1 + z2 * -1)
5 + -1z = 1 + (1 + -1z2)

Combine like terms: 1 + 1 = 2
5 + -1z = 2 + -1z2

Solving
5 + -1z = 2 + -1z2

Solving for variable 'z'.

Reorder the terms:
5 + -2 + -1z + z2 = 2 + -1z2 + -2 + z2

Combine like terms: 5 + -2 = 3
3 + -1z + z2 = 2 + -1z2 + -2 + z2

Reorder the terms:
3 + -1z + z2 = 2 + -2 + -1z2 + z2

Combine like terms: 2 + -2 = 0
3 + -1z + z2 = 0 + -1z2 + z2
3 + -1z + z2 = -1z2 + z2

Combine like terms: -1z2 + z2 = 0
3 + -1z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -1z + -3 + z2 = 0 + -3

Reorder the terms:
3 + -3 + -1z + z2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1z + z2 = 0 + -3
-1z + z2 = 0 + -3

Combine like terms: 0 + -3 = -3
-1z + z2 = -3

The z term is -1z.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1z + 0.25 + z2 = -3 + 0.25

Reorder the terms:
0.25 + -1z + z2 = -3 + 0.25

Combine like terms: -3 + 0.25 = -2.75
0.25 + -1z + z2 = -2.75

Factor a perfect square on the left side:
(z + -0.5)(z + -0.5) = -2.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.