What are the solutions to the equation completesquare 3x^2+5x+1 ?

The solutions to the equation completesquare 3x^2+5x+1 are 3(x+5/6)^2-13/12

Find the zeros of completesquare 3x^2+5x+1

The zeros of completesquare 3x^2+5x+1 are 3(x+5/6)^2-13/12

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complete the square

3 x^{2} + 5 x + 1

3 (x + \frac{5}{6})^{2} - \frac{13}{12}

Solution steps

3 x^{2} + 5 x + 1

Write

3 x^{2} + 5 x + 1

in the form:

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

Factor out

3

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

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

Add and subtract

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

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

Simplify

3 (x + \frac{5}{6})^{2} - \frac{13}{12}

x^{2} + 6^{2} = 9^{2}

2 x^{2} + 5 x = 5 x + 50

- 6 + 7 x + 3 x^{2} = 0

10 x^{2} - 3 x + 1

(2 x + 7)^{2} = 48

What are the solutions to the equation completesquare 3x^2+5x+1 ?
The solutions to the equation completesquare 3x^2+5x+1 are 3(x+5/6)^2-13/12
Find the zeros of completesquare 3x^2+5x+1
The zeros of completesquare 3x^2+5x+1 are 3(x+5/6)^2-13/12