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

The solutions to the equation completesquare 3x^2-2x-5 are 3(x-1/3)^2-16/3

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

The zeros of completesquare 3x^2-2x-5 are 3(x-1/3)^2-16/3

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complete the square

3 x^{2} - 2 x - 5

3 (x - \frac{1}{3})^{2} - \frac{16}{3}

Solution steps

3 x^{2} - 2 x - 5

Write

3 x^{2} - 2 x - 5

in the form:

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

Factor out

3

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

2 a = - \frac{2}{3} : a = - \frac{1}{3}

Add and subtract

(- \frac{1}{3})^{2}

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

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

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

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

Simplify

3 (x - \frac{1}{3})^{2} - \frac{16}{3}

(x) = - 3 x^{2} + 3000 x

460 = x^{2} + 3 x

(t^{2} D^{2} - t D) = 0

6 x^{2} - 12 x - 2 = 0

- 4 x^{2} - 16 = 0

What are the solutions to the equation completesquare 3x^2-2x-5 ?
The solutions to the equation completesquare 3x^2-2x-5 are 3(x-1/3)^2-16/3
Find the zeros of completesquare 3x^2-2x-5
The zeros of completesquare 3x^2-2x-5 are 3(x-1/3)^2-16/3