What are the solutions to the equation completesquare-1/5 x^2+4x+1 ?

The solutions to the equation completesquare-1/5 x^2+4x+1 are -1/5 (x-10)^2+21

Find the zeros of completesquare-1/5 x^2+4x+1

The zeros of completesquare-1/5 x^2+4x+1 are -1/5 (x-10)^2+21

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complete the square

- \frac{1}{5} x^{2} + 4 x + 1

- \frac{1}{5} (x - 10)^{2} + 21

Solution steps

- \frac{1}{5} x^{2} + 4 x + 1

Write in the standard form

a x^{2} + b x + c

- \frac{x ^{2}}{5} + 4 x + 1

Write

- \frac{x ^{2}}{5} + 4 x + 1

in the form:

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

Factor out

- \frac{1}{5}

- \frac{1}{5} (x^{2} - 20 x - 5)

2 a = - 20 : a = - 10

Add and subtract

(- 10)^{2}

- \frac{1}{5} (x^{2} - 20 x - 5 + (- 10)^{2} - (- 10)^{2})

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

x^{2} - 20 x + (- 10)^{2} = (x - 10)^{2}

- \frac{1}{5} ((x - 10)^{2} - 5 - (- 10)^{2})

Simplify

- \frac{1}{5} (x - 10)^{2} + 21

x, x^{2} + y^{2} + z = 0

1 = 9 - x^{2}

- 13 = x^{2} - 7 x

x^{2} - 11 x - 9 = 0

10 x^{2} + 13 x = 30

What are the solutions to the equation completesquare-1/5 x^2+4x+1 ?
The solutions to the equation completesquare-1/5 x^2+4x+1 are -1/5 (x-10)^2+21
Find the zeros of completesquare-1/5 x^2+4x+1
The zeros of completesquare-1/5 x^2+4x+1 are -1/5 (x-10)^2+21