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

The solutions to the equation completesquare x^2-x+1 are (x-1/2)^2+3/4

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

The zeros of completesquare x^2-x+1 are (x-1/2)^2+3/4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

complete the square

x^{2} - x + 1

(x - \frac{1}{2})^{2} + \frac{3}{4}

Solution steps

x^{2} - x + 1

Write

x^{2} - x + 1

in the form:

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

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

Add and subtract

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

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

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

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

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

Simplify

(x - \frac{1}{2})^{2} + \frac{3}{4}

x^{2} + (x + 2)^{2} = (x + 4)^{2}

x^{2} - 8 x = - 8

25 (5 + 2 x)^{2} + 14 = 30

8 x (x - 1) = 7 x^{2} + 4 x

2 x^{2} - 13 x + 25 = 0

What are the solutions to the equation completesquare x^2-x+1 ?
The solutions to the equation completesquare x^2-x+1 are (x-1/2)^2+3/4
Find the zeros of completesquare x^2-x+1
The zeros of completesquare x^2-x+1 are (x-1/2)^2+3/4