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

The solutions to the equation completesquare 3x^2-5x-2 are 3(x-5/6)^2-49/12

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

The zeros of completesquare 3x^2-5x-2 are 3(x-5/6)^2-49/12

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complete the square

3 x^{2} - 5 x - 2

3 (x - \frac{5}{6})^{2} - \frac{49}{12}

Solution steps

3 x^{2} - 5 x - 2

Write

3 x^{2} - 5 x - 2

in the form:

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

Factor out

3

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

Simplify

3 (x - \frac{5}{6})^{2} - \frac{49}{12}

m^{2} + 8 m + 15 = 0

x^{2} - 16 x - 36 = 0

3 x^{2} - 6 x - 5

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

x^{2} - 6 x + 5

What are the solutions to the equation completesquare 3x^2-5x-2 ?
The solutions to the equation completesquare 3x^2-5x-2 are 3(x-5/6)^2-49/12
Find the zeros of completesquare 3x^2-5x-2
The zeros of completesquare 3x^2-5x-2 are 3(x-5/6)^2-49/12