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

The solutions to the equation completesquare y^2+4ky+5 are (y+2k)^2+5-4k^2

Find the zeros of completesquare y^2+4ky+5

The zeros of completesquare y^2+4ky+5 are (y+2k)^2+5-4k^2

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complete the square

y^{2} + 4 k y + 5

(y + 2 k)^{2} + 5 - 4 k^{2}

Solution steps

y^{2} + 4 k y + 5

Complete the square using the formula:

a x^{2} + b x + c = (a x + \frac{b}{2 a})^{2} + c - \frac{b ^{2}}{4 a}

a = 1, b = 4 k, c = 5

(1 y + \frac{4 k}{2 1})^{2} + 5 - \frac{( 4 k ) ^{2}}{4 \cdot 1}

Refine

(y + 2 k)^{2} + 5 - 4 k^{2}

x^{2} - 14 x = 49

3 x^{2} + 24 x + 40 = 0

- 2 - 3 (x - 5)^{2} = - 29

(2 x - 1)^{2} - 16 = 9

x^{2} - x = 380

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