What are the solutions to the equation completesquare 6x^2+8x+9 ?

The solutions to the equation completesquare 6x^2+8x+9 are 6(x+2/3)^2+19/3

Find the zeros of completesquare 6x^2+8x+9

The zeros of completesquare 6x^2+8x+9 are 6(x+2/3)^2+19/3

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complete the square

6 x^{2} + 8 x + 9

6 (x + \frac{2}{3})^{2} + \frac{19}{3}

Solution steps

6 x^{2} + 8 x + 9

Write

6 x^{2} + 8 x + 9

in the form:

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

Factor out

6

6 (x^{2} + \frac{4 x}{3} + \frac{3}{2})

2 a = \frac{4}{3} : a = \frac{2}{3}

Add and subtract

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

6 (x^{2} + \frac{4 x}{3} + \frac{3}{2} + (\frac{2}{3})^{2} - (\frac{2}{3})^{2})

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

x^{2} + \frac{4}{3} x + (\frac{2}{3})^{2} = (x + \frac{2}{3})^{2}

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

Simplify

6 (x + \frac{2}{3})^{2} + \frac{19}{3}

x, f = a (x - h)^{2} + k

s^{2} + 2 s + 5

5 x^{2} - 2 = - 92

2 x^{2} + 12 x + 4

n^{2} - 7 n - 120 = 0

What are the solutions to the equation completesquare 6x^2+8x+9 ?
The solutions to the equation completesquare 6x^2+8x+9 are 6(x+2/3)^2+19/3
Find the zeros of completesquare 6x^2+8x+9
The zeros of completesquare 6x^2+8x+9 are 6(x+2/3)^2+19/3