What are the solutions to the equation completesquare 9x^2+6x+1 ?

The solutions to the equation completesquare 9x^2+6x+1 are 9(x+1/3)^2

Find the zeros of completesquare 9x^2+6x+1

The zeros of completesquare 9x^2+6x+1 are 9(x+1/3)^2

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complete the square

9 x^{2} + 6 x + 1

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

Solution steps

9 x^{2} + 6 x + 1

Write

9 x^{2} + 6 x + 1

in the form:

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

Factor out

9

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

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

Add and subtract

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

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

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

Simplify

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

x + 15 = x (x - 1)

(2 x + 1) (x - 4) - 10 = 0

x, x^{2} + 7 x = 0

0.544 x^{2} - 4.9 x + 7.385 = 0

4 x^{2} + 4 x + 6 = 0

What are the solutions to the equation completesquare 9x^2+6x+1 ?
The solutions to the equation completesquare 9x^2+6x+1 are 9(x+1/3)^2
Find the zeros of completesquare 9x^2+6x+1
The zeros of completesquare 9x^2+6x+1 are 9(x+1/3)^2