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

The solutions to the equation completesquare 2x^2+9x+9 are 2(x+9/4)^2-9/8

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

The zeros of completesquare 2x^2+9x+9 are 2(x+9/4)^2-9/8

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complete the square

2 x^{2} + 9 x + 9

2 (x + \frac{9}{4})^{2} - \frac{9}{8}

Solution steps

2 x^{2} + 9 x + 9

Write

2 x^{2} + 9 x + 9

in the form:

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

Factor out

2

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

2 a = \frac{9}{2} : a = \frac{9}{4}

Add and subtract

(\frac{9}{4})^{2}

2 (x^{2} + \frac{9 x}{2} + \frac{9}{2} + (\frac{9}{4})^{2} - (\frac{9}{4})^{2})

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

x^{2} + \frac{9}{2} x + (\frac{9}{4})^{2} = (x + \frac{9}{4})^{2}

2 ((x + \frac{9}{4})^{2} + \frac{9}{2} - (\frac{9}{4})^{2})

Simplify

2 (x + \frac{9}{4})^{2} - \frac{9}{8}

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

2 x^{2} + 9 x + 4

8 x^{2} - 2 (x + 10) = 10 x

(2 x + 1) (x - 2) = 5

x, x^{2} + y^{2} + 18 = 0

What are the solutions to the equation completesquare 2x^2+9x+9 ?
The solutions to the equation completesquare 2x^2+9x+9 are 2(x+9/4)^2-9/8
Find the zeros of completesquare 2x^2+9x+9
The zeros of completesquare 2x^2+9x+9 are 2(x+9/4)^2-9/8