What are the solutions to the equation completesquare x^2+8x+17 ?

The solutions to the equation completesquare x^2+8x+17 are (x+4)^2+1

Find the zeros of completesquare x^2+8x+17

The zeros of completesquare x^2+8x+17 are (x+4)^2+1

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complete the square

x^{2} + 8 x + 17

(x + 4)^{2} + 1

Solution steps

x^{2} + 8 x + 17

Write

x^{2} + 8 x + 17

in the form:

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

2 a = 8 : a = 4

Add and subtract

4^{2}

x^{2} + 8 x + 17 + 4^{2} - 4^{2}

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

x^{2} + 8 x + 4^{2} = (x + 4)^{2}

(x + 4)^{2} + 17 - 4^{2}

Simplify

(x + 4)^{2} + 1

x^{2} - 5 x + 2 = 0

\frac{1}{2} x^{2} + 4 x

x^{2} - 10 = 15

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

10 x = - 25 - x^{2}

What are the solutions to the equation completesquare x^2+8x+17 ?
The solutions to the equation completesquare x^2+8x+17 are (x+4)^2+1
Find the zeros of completesquare x^2+8x+17
The zeros of completesquare x^2+8x+17 are (x+4)^2+1