What are the solutions to the equation completesquare x^2+2/3 x+1 ?

The solutions to the equation completesquare x^2+2/3 x+1 are (x+1/3)^2+8/9

Find the zeros of completesquare x^2+2/3 x+1

The zeros of completesquare x^2+2/3 x+1 are (x+1/3)^2+8/9

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complete the square

x^{2} + \frac{2}{3} x + 1

(x + \frac{1}{3})^{2} + \frac{8}{9}

Solution steps

x^{2} + \frac{2}{3} x + 1

Write in the standard form

a x^{2} + b x + c

x^{2} + \frac{2 x}{3} + 1

Write

x^{2} + \frac{2 x}{3} + 1

in the form:

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

2 a = \frac{2}{3} : a = \frac{1}{3}

Add and subtract

(\frac{1}{3})^{2}

x^{2} + \frac{2 x}{3} + 1 + (\frac{1}{3})^{2} - (\frac{1}{3})^{2}

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

x^{2} + \frac{2}{3} x + (\frac{1}{3})^{2} = (x + \frac{1}{3})^{2}

(x + \frac{1}{3})^{2} + 1 - (\frac{1}{3})^{2}

Simplify

(x + \frac{1}{3})^{2} + \frac{8}{9}

x^{2} - 5 x - 36 = 0

x^{2} + 10 x + 21 = 0

x^{2} - 15 = 106

4 (x^{2} - 7) + 27 = - 12 x^{2}

x^{2} - 3 x = 6

What are the solutions to the equation completesquare x^2+2/3 x+1 ?
The solutions to the equation completesquare x^2+2/3 x+1 are (x+1/3)^2+8/9
Find the zeros of completesquare x^2+2/3 x+1
The zeros of completesquare x^2+2/3 x+1 are (x+1/3)^2+8/9