What are the solutions to the equation completesquare x^2+x+5 ?

The solutions to the equation completesquare x^2+x+5 are (x+1/2)^2+19/4

Find the zeros of completesquare x^2+x+5

The zeros of completesquare x^2+x+5 are (x+1/2)^2+19/4

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complete the square

x^{2} + x + 5

(x + \frac{1}{2})^{2} + \frac{19}{4}

Solution steps

x^{2} + x + 5

Write

x^{2} + x + 5

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 + 5 + (\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} + 5 - (\frac{1}{2})^{2}

Simplify

(x + \frac{1}{2})^{2} + \frac{19}{4}

9 (x^{2} - 14) - 12 = - 17

20 x^{2} = - 25 x

6 x^{2} - x = 1

m^{2} = 14

3 x^{2} = 5 x - 6

What are the solutions to the equation completesquare x^2+x+5 ?
The solutions to the equation completesquare x^2+x+5 are (x+1/2)^2+19/4
Find the zeros of completesquare x^2+x+5
The zeros of completesquare x^2+x+5 are (x+1/2)^2+19/4