What are the solutions to the equation completesquare 3x^2-4x+5 ?

The solutions to the equation completesquare 3x^2-4x+5 are 3(x-2/3)^2+11/3

Find the zeros of completesquare 3x^2-4x+5

The zeros of completesquare 3x^2-4x+5 are 3(x-2/3)^2+11/3

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complete the square

3 x^{2} - 4 x + 5

3 (x - \frac{2}{3})^{2} + \frac{11}{3}

Solution steps

3 x^{2} - 4 x + 5

Write

3 x^{2} - 4 x + 5

in the form:

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

Factor out

3

3 (x^{2} - \frac{4 x}{3} + \frac{5}{3})

2 a = - \frac{4}{3} : a = - \frac{2}{3}

Add and subtract

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

3 (x^{2} - \frac{4 x}{3} + \frac{5}{3} + (- \frac{2}{3})^{2} - (- \frac{2}{3})^{2})

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

x^{2} - \frac{4}{3} x + (- \frac{2}{3})^{2} = (x - \frac{2}{3})^{2}

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

Simplify

3 (x - \frac{2}{3})^{2} + \frac{11}{3}

10 x - 5 - x^{2} = 16 x - 10 - 2 x^{2}

x, x (1 - x) y^{n} + (\frac{3}{2} - 2 x) y^{1} + 2 y = 0

x^{2} + 11 x - 522 = 0

x^{2} - x = x - 1

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

What are the solutions to the equation completesquare 3x^2-4x+5 ?
The solutions to the equation completesquare 3x^2-4x+5 are 3(x-2/3)^2+11/3
Find the zeros of completesquare 3x^2-4x+5
The zeros of completesquare 3x^2-4x+5 are 3(x-2/3)^2+11/3