What are the solutions to the equation completesquare 3x^2-6x+5 ?

The solutions to the equation completesquare 3x^2-6x+5 are 3(x-1)^2+2

Find the zeros of completesquare 3x^2-6x+5

The zeros of completesquare 3x^2-6x+5 are 3(x-1)^2+2

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complete the square

3 x^{2} - 6 x + 5

3 (x - 1)^{2} + 2

Solution steps

3 x^{2} - 6 x + 5

Write

3 x^{2} - 6 x + 5

in the form:

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

Factor out

3

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

2 a = - 2 : a = - 1

Add and subtract

(- 1)^{2}

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

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

x^{2} - 2 x + (- 1)^{2} = (x - 1)^{2}

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

Simplify

3 (x - 1)^{2} + 2

x^{2} = - 4 x - 4

x^{2} - 18 x + 10 = 0

x^{2} - 4 x + 24 = 0

x^{2} - 18 x + 401 = 0

(6 x - 4) (3 x + 5) = (4 x - 9) (3 x + 5)

What are the solutions to the equation completesquare 3x^2-6x+5 ?
The solutions to the equation completesquare 3x^2-6x+5 are 3(x-1)^2+2
Find the zeros of completesquare 3x^2-6x+5
The zeros of completesquare 3x^2-6x+5 are 3(x-1)^2+2