What are the solutions to the equation z^2+6z=r^2-9 ?

The solutions to the equation z^2+6z=r^2-9 are z=-r-3,z=r-3

Find the zeros of z^2+6z=r^2-9

The zeros of z^2+6z=r^2-9 are z=-r-3,z=r-3

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z^{2} + 6 z = r^{2} - 9

z = - r - 3, z = r - 3

Solution steps

z^{2} + 6 z = r^{2} - 9

Move

9

to the left side

z^{2} + 6 z + 9 = r^{2}

Move

r^{2}

to the left side

z^{2} + 6 z + 9 - r^{2} = 0

Factor

z^{2} + 6 z + 9 - r^{2} : (z + r + 3) (z - r + 3)

(z + r + 3) (z - r + 3) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

z + r + 3 = 0 or z - r + 3 = 0

Solve

z + r + 3 = 0 : z = - r - 3

Solve

z - r + 3 = 0 : z = r - 3

The solutions to the quadratic equation are:

z = - r - 3, z = r - 3

X^{2} = 4^{2} + 1 6^{2}

s^{2} - 14 s + 53

2 X (X - 1) = 4 X - 3

5 x^{2} - 9 = 4 x

5 y - 6 + 50 y^{2} = 0

What are the solutions to the equation z^2+6z=r^2-9 ?
The solutions to the equation z^2+6z=r^2-9 are z=-r-3,z=r-3
Find the zeros of z^2+6z=r^2-9
The zeros of z^2+6z=r^2-9 are z=-r-3,z=r-3