What are the solutions to the equation completesquare 8z^2+5z ?

The solutions to the equation completesquare 8z^2+5z are 8(z+5/16)^2-25/32

Find the zeros of completesquare 8z^2+5z

The zeros of completesquare 8z^2+5z are 8(z+5/16)^2-25/32

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complete the square

8 z^{2} + 5 z

8 (z + \frac{5}{16})^{2} - \frac{25}{32}

Solution steps

8 z^{2} + 5 z

Write

8 z^{2} + 5 z

in the form:

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

Factor out

8

8 (z^{2} + \frac{5 z}{8})

2 a = \frac{5}{8} : a = \frac{5}{16}

Add and subtract

(\frac{5}{16})^{2}

8 (z^{2} + \frac{5 z}{8} + (\frac{5}{16})^{2} - (\frac{5}{16})^{2})

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

z^{2} + \frac{5}{8} z + (\frac{5}{16})^{2} = (z + \frac{5}{16})^{2}

8 ((z + \frac{5}{16})^{2} - (\frac{5}{16})^{2})

Simplify

8 (z + \frac{5}{16})^{2} - \frac{25}{32}

x, (x - 3)^{2} + (y - 5)^{2} = 0

x^{2} + 11 x + 24 = 0

2 x^{2} - 5 x - 3 = 0

18 k^{2} = 50

x^{2} - 10 x - 3

What are the solutions to the equation completesquare 8z^2+5z ?
The solutions to the equation completesquare 8z^2+5z are 8(z+5/16)^2-25/32
Find the zeros of completesquare 8z^2+5z
The zeros of completesquare 8z^2+5z are 8(z+5/16)^2-25/32