What are the solutions to the equation x^2-3(x-3)^2=2 ?

The solutions to the equation x^2-3(x-3)^2=2 are x=(9-sqrt(23))/2 ,x=(9+sqrt(23))/2

Find the zeros of x^2-3(x-3)^2=2

The zeros of x^2-3(x-3)^2=2 are x=(9-sqrt(23))/2 ,x=(9+sqrt(23))/2

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

x = \frac{9 - 23}{2}, x = \frac{9 + 23}{2}

Decimal Notation

x = 2.10208 \dots, x = 6.89791 \dots

Solution steps

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

Expand

x^{2} - 3 (x - 3)^{2} : - 2 x^{2} + 18 x - 27

- 2 x^{2} + 18 x - 27 = 2

Move

2

to the left side

- 2 x^{2} + 18 x - 29 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 18 \pm 1 8 ^{2} - 4 ( - 2 ) ( - 29 )}{2 ( - 2 )}

1 8^{2} - 4 (- 2) (- 29) = 223

x_{1, 2} = \frac{- 18 \pm 2 23}{2 ( - 2 )}

Separate the solutions

x_{1} = \frac{- 18 + 2 23}{2 ( - 2 )}, x_{2} = \frac{- 18 - 2 23}{2 ( - 2 )}

x = \frac{- 18 + 2 23}{2 ( - 2 )} : \frac{9 - 23}{2}

x = \frac{- 18 - 2 23}{2 ( - 2 )} : \frac{9 + 23}{2}

The solutions to the quadratic equation are:

x = \frac{9 - 23}{2}, x = \frac{9 + 23}{2}

x^{2} - 8

4 x^{2} + 1

x^{2} + 8 x = 9

5 x^{2} + 15 x = 40

0 = 0.5 F (1 - \frac{F}{3000})

What are the solutions to the equation x^2-3(x-3)^2=2 ?
The solutions to the equation x^2-3(x-3)^2=2 are x=(9-sqrt(23))/2 ,x=(9+sqrt(23))/2
Find the zeros of x^2-3(x-3)^2=2
The zeros of x^2-3(x-3)^2=2 are x=(9-sqrt(23))/2 ,x=(9+sqrt(23))/2