What are the solutions to the equation completesquare-x^2-4x+1 ?

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

Find the zeros of completesquare-x^2-4x+1

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

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complete the square

- x^{2} - 4 x + 1

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

Solution steps

- x^{2} - 4 x + 1

Write

- x^{2} - 4 x + 1

in the form:

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

Factor out

- 1

- (x^{2} + 4 x - 1)

2 a = 4 : a = 2

Add and subtract

2^{2}

- (x^{2} + 4 x - 1 + 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} - 1 - 2^{2})

Simplify

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

4 x (2 - x) = 0

(5 x + 2) (x - 1) = 7 x

t^{2} + 3 t + 2 = 0

(x - 1)^{2} = 14

\frac{1}{4} (2 x - 12)^{2} + 8 = 4

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