What are the solutions to the equation completesquare 2x^2+3x ?

The solutions to the equation completesquare 2x^2+3x are 2(x+3/4)^2-9/8

Find the zeros of completesquare 2x^2+3x

The zeros of completesquare 2x^2+3x are 2(x+3/4)^2-9/8

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complete the square

2 x^{2} + 3 x

2 (x + \frac{3}{4})^{2} - \frac{9}{8}

Solution steps

2 x^{2} + 3 x

Write

2 x^{2} + 3 x

in the form:

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

Factor out

2

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

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

Add and subtract

(\frac{3}{4})^{2}

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

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

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

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

Simplify

2 (x + \frac{3}{4})^{2} - \frac{9}{8}

- 5 x^{2} - 30 x - 150 = 0

x^{2} + x - 182 = 0

6 x^{2} = 54 x

x (x - 6) = 7

x + 15 = \frac{( x - 9 ) ^{2}}{2}

What are the solutions to the equation completesquare 2x^2+3x ?
The solutions to the equation completesquare 2x^2+3x are 2(x+3/4)^2-9/8
Find the zeros of completesquare 2x^2+3x
The zeros of completesquare 2x^2+3x are 2(x+3/4)^2-9/8