What are the solutions to the equation completesquare 3x^2-6x+11 ?

The solutions to the equation completesquare 3x^2-6x+11 are 3(x-1)^2+8

Find the zeros of completesquare 3x^2-6x+11

The zeros of completesquare 3x^2-6x+11 are 3(x-1)^2+8

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complete the square

3 x^{2} - 6 x + 11

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

Solution steps

3 x^{2} - 6 x + 11

Write

3 x^{2} - 6 x + 11

in the form:

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

Factor out

3

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

2 a = - 2 : a = - 1

Add and subtract

(- 1)^{2}

3 (x^{2} - 2 x + \frac{11}{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{11}{3} - (- 1)^{2})

Simplify

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

7 - x^{2} = x

x^{2} + 22 x = 8 x - 53

\frac{x ( x + 1 )}{2} = 120

x^{2} - 37 x + 27 = 0

7 x^{2} - 66 x + 27 = 0

What are the solutions to the equation completesquare 3x^2-6x+11 ?
The solutions to the equation completesquare 3x^2-6x+11 are 3(x-1)^2+8
Find the zeros of completesquare 3x^2-6x+11
The zeros of completesquare 3x^2-6x+11 are 3(x-1)^2+8