What are the solutions to the equation completesquare x^2+2/5 x+9 ?

The solutions to the equation completesquare x^2+2/5 x+9 are (x+1/5)^2+224/25

Find the zeros of completesquare x^2+2/5 x+9

The zeros of completesquare x^2+2/5 x+9 are (x+1/5)^2+224/25

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complete the square

x^{2} + \frac{2}{5} x + 9

(x + \frac{1}{5})^{2} + \frac{224}{25}

Solution steps

x^{2} + \frac{2}{5} x + 9

Write in the standard form

a x^{2} + b x + c

x^{2} + \frac{2 x}{5} + 9

Write

x^{2} + \frac{2 x}{5} + 9

in the form:

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

2 a = \frac{2}{5} : a = \frac{1}{5}

Add and subtract

(\frac{1}{5})^{2}

x^{2} + \frac{2 x}{5} + 9 + (\frac{1}{5})^{2} - (\frac{1}{5})^{2}

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

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

(x + \frac{1}{5})^{2} + 9 - (\frac{1}{5})^{2}

Simplify

(x + \frac{1}{5})^{2} + \frac{224}{25}

x^{2} + 22 x + 28 = 12 x

2 x^{2} - 5 x - 3 = 2 x - 4 x^{2}

2 (2 x + 1)^{2} = (x + 3)^{2} - 10

x^{2} - 2 x = 3

7 x^{2} - 18 = 45

What are the solutions to the equation completesquare x^2+2/5 x+9 ?
The solutions to the equation completesquare x^2+2/5 x+9 are (x+1/5)^2+224/25
Find the zeros of completesquare x^2+2/5 x+9
The zeros of completesquare x^2+2/5 x+9 are (x+1/5)^2+224/25