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}

(6 x - 3) (2 x + 4) = 3

4 x^{2} - 2 x + 10 = 0

x^{2} + 9 x = 27

2 x^{2} - 10 x + 9 = 0

2 a^{2} - a + [2 (a - 1) (a + 3)] = 26

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