What are the solutions to the equation completesquare 3x^2-x+8 ?

The solutions to the equation completesquare 3x^2-x+8 are 3(x-1/6)^2+95/12

Find the zeros of completesquare 3x^2-x+8

The zeros of completesquare 3x^2-x+8 are 3(x-1/6)^2+95/12

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complete the square

3 x^{2} - x + 8

3 (x - \frac{1}{6})^{2} + \frac{95}{12}

Solution steps

3 x^{2} - x + 8

Write

3 x^{2} - x + 8

in the form:

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

Factor out

3

3 (x^{2} - \frac{x}{3} + \frac{8}{3})

2 a = - \frac{1}{3} : a = - \frac{1}{6}

Add and subtract

(- \frac{1}{6})^{2}

3 (x^{2} - \frac{x}{3} + \frac{8}{3} + (- \frac{1}{6})^{2} - (- \frac{1}{6})^{2})

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

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

3 ((x - \frac{1}{6})^{2} + \frac{8}{3} - (- \frac{1}{6})^{2})

Simplify

3 (x - \frac{1}{6})^{2} + \frac{95}{12}

2 x^{2} + 8 x - 34 = 0

3 x^{2} + 4 x = - 1

- 6 x^{2} + 2 = 0

3 x^{2} + x - 102 = 0

1 - x^{2}

What are the solutions to the equation completesquare 3x^2-x+8 ?
The solutions to the equation completesquare 3x^2-x+8 are 3(x-1/6)^2+95/12
Find the zeros of completesquare 3x^2-x+8
The zeros of completesquare 3x^2-x+8 are 3(x-1/6)^2+95/12