What are the solutions to the equation completesquare x^2+2/3 x+5 ?

The solutions to the equation completesquare x^2+2/3 x+5 are (x+1/3)^2+44/9

Find the zeros of completesquare x^2+2/3 x+5

The zeros of completesquare x^2+2/3 x+5 are (x+1/3)^2+44/9

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complete the square

x^{2} + \frac{2}{3} x + 5

(x + \frac{1}{3})^{2} + \frac{44}{9}

Solution steps

x^{2} + \frac{2}{3} x + 5

Write in the standard form

a x^{2} + b x + c

x^{2} + \frac{2 x}{3} + 5

Write

x^{2} + \frac{2 x}{3} + 5

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} + 5 + (\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} + 5 - (\frac{1}{3})^{2}

Simplify

(x + \frac{1}{3})^{2} + \frac{44}{9}

2 x^{2} - 5 = - 3 x

5 x^{2} - 10 x + 3

(7 x + 8) (2 x - 11) = 0

x^{2} - 5 = - 4

A, B = A^{2} - 3 A + 21

What are the solutions to the equation completesquare x^2+2/3 x+5 ?
The solutions to the equation completesquare x^2+2/3 x+5 are (x+1/3)^2+44/9
Find the zeros of completesquare x^2+2/3 x+5
The zeros of completesquare x^2+2/3 x+5 are (x+1/3)^2+44/9