What are the solutions to the equation completesquare x^2-4/5 x-1 ?

The solutions to the equation completesquare x^2-4/5 x-1 are (x-2/5)^2-29/25

Find the zeros of completesquare x^2-4/5 x-1

The zeros of completesquare x^2-4/5 x-1 are (x-2/5)^2-29/25

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complete the square

x^{2} - \frac{4}{5} x - 1

(x - \frac{2}{5})^{2} - \frac{29}{25}

Solution steps

x^{2} - \frac{4}{5} x - 1

Write in the standard form

a x^{2} + b x + c

x^{2} - \frac{4 x}{5} - 1

Write

x^{2} - \frac{4 x}{5} - 1

in the form:

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

2 a = - \frac{4}{5} : a = - \frac{2}{5}

Add and subtract

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

x^{2} - \frac{4 x}{5} - 1 + (- \frac{2}{5})^{2} - (- \frac{2}{5})^{2}

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

x^{2} - \frac{4}{5} x + (- \frac{2}{5})^{2} = (x - \frac{2}{5})^{2}

(x - \frac{2}{5})^{2} - 1 - (- \frac{2}{5})^{2}

Simplify

(x - \frac{2}{5})^{2} - \frac{29}{25}

z^{2} - 2 z

z^{2} + 3 z - 7 = z

x^{2} + 2 x - 8 = 0

3 x^{2} - 7 = 5

7 k = 78 - k^{2}

What are the solutions to the equation completesquare x^2-4/5 x-1 ?
The solutions to the equation completesquare x^2-4/5 x-1 are (x-2/5)^2-29/25
Find the zeros of completesquare x^2-4/5 x-1
The zeros of completesquare x^2-4/5 x-1 are (x-2/5)^2-29/25