What are the solutions to the equation completesquare x^2+1/2 x+3 ?

The solutions to the equation completesquare x^2+1/2 x+3 are (x+1/4)^2+47/16

Find the zeros of completesquare x^2+1/2 x+3

The zeros of completesquare x^2+1/2 x+3 are (x+1/4)^2+47/16

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complete the square

x^{2} + \frac{1}{2} x + 3

(x + \frac{1}{4})^{2} + \frac{47}{16}

Solution steps

x^{2} + \frac{1}{2} x + 3

Write in the standard form

a x^{2} + b x + c

x^{2} + \frac{x}{2} + 3

Write

x^{2} + \frac{x}{2} + 3

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

Simplify

(x + \frac{1}{4})^{2} + \frac{47}{16}

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

4 (x^{2} - 4) - 5 (3 + 2 x) = - 7

(x - 7) (x + 4) = 0

3 (2 x - 5)^{2} - 15 = 48

- 3 x^{2} - 3 x - 9 = - 2

What are the solutions to the equation completesquare x^2+1/2 x+3 ?
The solutions to the equation completesquare x^2+1/2 x+3 are (x+1/4)^2+47/16
Find the zeros of completesquare x^2+1/2 x+3
The zeros of completesquare x^2+1/2 x+3 are (x+1/4)^2+47/16