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

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

Find the zeros of completesquare x^2+5x+1

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

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complete the square

x^{2} + 5 x + 1

(x + \frac{5}{2})^{2} - \frac{21}{4}

Solution steps

x^{2} + 5 x + 1

Write

x^{2} + 5 x + 1

in the form:

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

2 a = 5 : a = \frac{5}{2}

Add and subtract

(\frac{5}{2})^{2}

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

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

x^{2} + 5 x + (\frac{5}{2})^{2} = (x + \frac{5}{2})^{2}

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

Simplify

(x + \frac{5}{2})^{2} - \frac{21}{4}

5 k^{2} - 9 k + 18 = 4 k^{2}

s^{2} + 4 s + 13

3 x^{2} + 66 = - 30 x

s^{2} + 4 s + 5

6 x^{2} + 48 x + 90 = 0

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