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

The solutions to the equation completesquare 2x^2+5x+2 are 2(x+5/4)^2-9/8

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

The zeros of completesquare 2x^2+5x+2 are 2(x+5/4)^2-9/8

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complete the square

2 x^{2} + 5 x + 2

2 (x + \frac{5}{4})^{2} - \frac{9}{8}

Solution steps

2 x^{2} + 5 x + 2

Write

2 x^{2} + 5 x + 2

in the form:

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

Factor out

2

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

2 a = \frac{5}{2} : a = \frac{5}{4}

Add and subtract

(\frac{5}{4})^{2}

2 (x^{2} + \frac{5 x}{2} + 1 + (\frac{5}{4})^{2} - (\frac{5}{4})^{2})

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

x^{2} + \frac{5}{2} x + (\frac{5}{4})^{2} = (x + \frac{5}{4})^{2}

2 ((x + \frac{5}{4})^{2} + 1 - (\frac{5}{4})^{2})

Simplify

2 (x + \frac{5}{4})^{2} - \frac{9}{8}

x, x y + 2 x + 3 x^{2} = 4

\frac{4}{3} x^{2} = \frac{2}{3} x^{2} + 6

x^{2} - 2 x - 4

x^{2} - 2 x - 2

x^{2} - 2 x + 3

What are the solutions to the equation completesquare 2x^2+5x+2 ?
The solutions to the equation completesquare 2x^2+5x+2 are 2(x+5/4)^2-9/8
Find the zeros of completesquare 2x^2+5x+2
The zeros of completesquare 2x^2+5x+2 are 2(x+5/4)^2-9/8