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

d = \frac{1}{2} a t^{2}

- 4 x^{2} - 20 x - 25 = 0

3 x^{2} - 2 x - 2 = 4

(6 x - 5) (2 x - 9) = 0

4 a^{2} + 6 a - 6 = - 3

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