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

The solutions to the equation completesquare x^2-1/2 x are (x-1/4)^2-1/16

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

The zeros of completesquare x^2-1/2 x are (x-1/4)^2-1/16

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complete the square

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

(x - \frac{1}{4})^{2} - \frac{1}{16}

Solution steps

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

Write in the standard form

a x^{2} + b x + c

x^{2} - \frac{x}{2}

Write

x^{2} - \frac{x}{2}

in the form:

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

2 a = - \frac{1}{2} : a = - \frac{1}{4}

Add and subtract

(- \frac{1}{4})^{2}

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

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

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

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

Simplify

(x - \frac{1}{4})^{2} - \frac{1}{16}

(3 x - 5)^{2} = 49

x^{2} - 6 x + 10 = 0

2 x^{2} + 14 x + 3 = - 17

2 x^{2} - 14 x + 1 = 0

x^{2} - 4 x = 0

What are the solutions to the equation completesquare x^2-1/2 x ?
The solutions to the equation completesquare x^2-1/2 x are (x-1/4)^2-1/16
Find the zeros of completesquare x^2-1/2 x
The zeros of completesquare x^2-1/2 x are (x-1/4)^2-1/16