What are the solutions to the equation completesquare 3x^2+5x+3 ?

The solutions to the equation completesquare 3x^2+5x+3 are 3(x+5/6)^2+11/12

Find the zeros of completesquare 3x^2+5x+3

The zeros of completesquare 3x^2+5x+3 are 3(x+5/6)^2+11/12

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complete the square

3 x^{2} + 5 x + 3

3 (x + \frac{5}{6})^{2} + \frac{11}{12}

Solution steps

3 x^{2} + 5 x + 3

Write

3 x^{2} + 5 x + 3

in the form:

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

Factor out

3

3 (x^{2} + \frac{5 x}{3} + 1)

2 a = \frac{5}{3} : a = \frac{5}{6}

Add and subtract

(\frac{5}{6})^{2}

3 (x^{2} + \frac{5 x}{3} + 1 + (\frac{5}{6})^{2} - (\frac{5}{6})^{2})

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

x^{2} + \frac{5}{3} x + (\frac{5}{6})^{2} = (x + \frac{5}{6})^{2}

3 ((x + \frac{5}{6})^{2} + 1 - (\frac{5}{6})^{2})

Simplify

3 (x + \frac{5}{6})^{2} + \frac{11}{12}

3 x - 6 = - x^{2}

0.1 n^{2} + 100 n + 8 = 60000

x, x^{2} y^{3} = 6^{12}

4.68 x^{2} - 15.5 x + 12.43 = 0

3 x + 18 = x^{2}

What are the solutions to the equation completesquare 3x^2+5x+3 ?
The solutions to the equation completesquare 3x^2+5x+3 are 3(x+5/6)^2+11/12
Find the zeros of completesquare 3x^2+5x+3
The zeros of completesquare 3x^2+5x+3 are 3(x+5/6)^2+11/12