What are the solutions to the equation completesquare z^2+6z ?

The solutions to the equation completesquare z^2+6z are (z+3)^2-9

Find the zeros of completesquare z^2+6z

The zeros of completesquare z^2+6z are (z+3)^2-9

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complete the square

z^{2} + 6 z

(z + 3)^{2} - 9

Solution steps

z^{2} + 6 z

Write

z^{2} + 6 z

in the form:

x^{2} + 2 a x + a^{2}

2 a = 6 : a = 3

Add and subtract

3^{2}

z^{2} + 6 z + 3^{2} - 3^{2}

x^{2} + 2 a x + a^{2} = (x + a)^{2}

z^{2} + 6 z + 3^{2} = (z + 3)^{2}

(z + 3)^{2} - 3^{2}

Simplify

(z + 3)^{2} - 9

x^{2} + 4 x + 19 = 0

(x - 2)^{2} - (2 x + 3)^{2} = 0

x^{2} - (- 2) x - 24 = 0

n^{2} + 9 n + 14 = 0

x^{2} + 3.9 x + 6.8 = 0

What are the solutions to the equation completesquare z^2+6z ?
The solutions to the equation completesquare z^2+6z are (z+3)^2-9
Find the zeros of completesquare z^2+6z
The zeros of completesquare z^2+6z are (z+3)^2-9