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

The solutions to the equation completesquare x^2-1/2 x+1 are (x-1/4)^2+15/16

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

The zeros of completesquare x^2-1/2 x+1 are (x-1/4)^2+15/16

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complete the square

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

(x - \frac{1}{4})^{2} + \frac{15}{16}

Solution steps

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

Write in the standard form

a x^{2} + b x + c

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

Write

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

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

Simplify

(x - \frac{1}{4})^{2} + \frac{15}{16}

(x + 1)^{2} = 11

x^{2} + 13 = 17

- x^{2} + 12 x - 36 = 0

x^{2} + 4 x + 7 = 15

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

What are the solutions to the equation completesquare x^2-1/2 x+1 ?
The solutions to the equation completesquare x^2-1/2 x+1 are (x-1/4)^2+15/16
Find the zeros of completesquare x^2-1/2 x+1
The zeros of completesquare x^2-1/2 x+1 are (x-1/4)^2+15/16