What are the solutions to the equation completesquare x^2-x+3 ?

The solutions to the equation completesquare x^2-x+3 are (x-1/2)^2+11/4

Find the zeros of completesquare x^2-x+3

The zeros of completesquare x^2-x+3 are (x-1/2)^2+11/4

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complete the square

x^{2} - x + 3

(x - \frac{1}{2})^{2} + \frac{11}{4}

Solution steps

x^{2} - x + 3

Write

x^{2} - x + 3

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

Simplify

(x - \frac{1}{2})^{2} + \frac{11}{4}

x^{2} - x + 4

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

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

6 x^{2} - 12 x - 2

9 x^{2} - 72 x = 0

What are the solutions to the equation completesquare x^2-x+3 ?
The solutions to the equation completesquare x^2-x+3 are (x-1/2)^2+11/4
Find the zeros of completesquare x^2-x+3
The zeros of completesquare x^2-x+3 are (x-1/2)^2+11/4