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

The solutions to the equation completesquare p^2+p+1 are (p+1/2)^2+3/4

Find the zeros of completesquare p^2+p+1

The zeros of completesquare p^2+p+1 are (p+1/2)^2+3/4

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complete the square

p^{2} + p + 1

(p + \frac{1}{2})^{2} + \frac{3}{4}

Solution steps

p^{2} + p + 1

Write

p^{2} + p + 1

in the form:

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

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

Add and subtract

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

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

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

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

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

Simplify

(p + \frac{1}{2})^{2} + \frac{3}{4}

- 3 x - 17 = x^{2} - 2

9 b^{2} + 8 b = - 2

0 = - (x + 5)^{2} - 1

(4 a + 5) 2 = 16 a^{2} + B a + 25

x^{2} - 3 \cdot x + 2 = 0

What are the solutions to the equation completesquare p^2+p+1 ?
The solutions to the equation completesquare p^2+p+1 are (p+1/2)^2+3/4
Find the zeros of completesquare p^2+p+1
The zeros of completesquare p^2+p+1 are (p+1/2)^2+3/4