What are the solutions to the equation completesquare 3/4 x^2+x ?

The solutions to the equation completesquare 3/4 x^2+x are 3/4 (x+2/3)^2-1/3

Find the zeros of completesquare 3/4 x^2+x

The zeros of completesquare 3/4 x^2+x are 3/4 (x+2/3)^2-1/3

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complete the square

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

\frac{3}{4} (x + \frac{2}{3})^{2} - \frac{1}{3}

Solution steps

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

Write in the standard form

a x^{2} + b x + c

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

Write

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

in the form:

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

Factor out

\frac{3}{4}

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

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

Add and subtract

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

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

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

Simplify

\frac{3}{4} (x + \frac{2}{3})^{2} - \frac{1}{3}

0 = - x^{2} + 5 x - 6

18 x^{2} - 144 x + 216 = 0

- 2 x^{2} - 18 x - 81 = - x^{2}

6 q^{2} - 8 q = 0

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

What are the solutions to the equation completesquare 3/4 x^2+x ?
The solutions to the equation completesquare 3/4 x^2+x are 3/4 (x+2/3)^2-1/3
Find the zeros of completesquare 3/4 x^2+x
The zeros of completesquare 3/4 x^2+x are 3/4 (x+2/3)^2-1/3