What are the solutions to the equation completesquare n^2+n ?

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

Find the zeros of completesquare n^2+n

The zeros of completesquare n^2+n are (n+1/2)^2-1/4

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complete the square

n^{2} + n

(n + \frac{1}{2})^{2} - \frac{1}{4}

Solution steps

n^{2} + n

Write

n^{2} + n

in the form:

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

2 a = 1 : a = \frac{1}{2}

Add and subtract

(\frac{1}{2})^{2}

n^{2} + n + (\frac{1}{2})^{2} - (\frac{1}{2})^{2}

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

n^{2} + 1 n + (\frac{1}{2})^{2} = (n + \frac{1}{2})^{2}

(n + \frac{1}{2})^{2} - (\frac{1}{2})^{2}

Simplify

(n + \frac{1}{2})^{2} - \frac{1}{4}

y^{2} = 5 y - 4

s^{2} + 4 s + 12

x^{2} - \frac{25}{4} = 0

x, 2 x^{2} - 3 x - 15 = 0

- 7 x + x^{2} = 0

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