What are the solutions to the equation completesquare x^2+4x+5 ?

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

Find the zeros of completesquare x^2+4x+5

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

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complete the square

x^{2} + 4 x + 5

(x + 2)^{2} + 1

Solution steps

x^{2} + 4 x + 5

Write

x^{2} + 4 x + 5

in the form:

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

2 a = 4 : a = 2

Add and subtract

2^{2}

x^{2} + 4 x + 5 + 2^{2} - 2^{2}

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

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

(x + 2)^{2} + 5 - 2^{2}

Simplify

(x + 2)^{2} + 1

(x + 10)^{2} = 64

6 - x^{2} = - 8

x^{2} - 8 = 1

(x - 5)^{2} + 8 (x - 5) + 15 = 0

10 - x^{2} = - 27

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