What are the solutions to the equation (9-x^2)/9 =x^2-4x+4 ?

The solutions to the equation (9-x^2)/9 =x^2-4x+4 are x=(3(6+sqrt(6)))/(10),x=(3(6-sqrt(6)))/(10)

Find the zeros of (9-x^2)/9 =x^2-4x+4

The zeros of (9-x^2)/9 =x^2-4x+4 are x=(3(6+sqrt(6)))/(10),x=(3(6-sqrt(6)))/(10)

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\frac{9 - x ^{2}}{9} = x^{2} - 4 x + 4

x = \frac{3 ( 6 + 6 )}{10}, x = \frac{3 ( 6 - 6 )}{10}

Decimal Notation

x = 2.53484 \dots, x = 1.06515 \dots

Solution steps

\frac{9 - x ^{2}}{9} = x^{2} - 4 x + 4

Multiply both sides by

9

9 - x^{2} = 9 x^{2} - 36 x + 36

Switch sides

9 x^{2} - 36 x + 36 = 9 - x^{2}

Move

x^{2}

to the left side

10 x^{2} - 36 x + 36 = 9

Move

9

to the left side

10 x^{2} - 36 x + 27 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 36 ) \pm ( - 36 ) ^{2} - 4 \cdot 10 \cdot 27}{2 \cdot 10}

(- 36)^{2} - 4 \cdot 10 \cdot 27 = 66

x_{1, 2} = \frac{- ( - 36 ) \pm 6 6}{2 \cdot 10}

Separate the solutions

x_{1} = \frac{- ( - 36 ) + 6 6}{2 \cdot 10}, x_{2} = \frac{- ( - 36 ) - 6 6}{2 \cdot 10}

x = \frac{- ( - 36 ) + 6 6}{2 \cdot 10} : \frac{3 ( 6 + 6 )}{10}

x = \frac{- ( - 36 ) - 6 6}{2 \cdot 10} : \frac{3 ( 6 - 6 )}{10}

The solutions to the quadratic equation are:

x = \frac{3 ( 6 + 6 )}{10}, x = \frac{3 ( 6 - 6 )}{10}

2 x + x^{2} = 7 x

(x + 6) (x - 2) = - 7

98 x - 49 x^{2} - 45

6 a^{2} - 7 ab - 3 b^{2}

What are the solutions to the equation (9-x^2)/9 =x^2-4x+4 ?
The solutions to the equation (9-x^2)/9 =x^2-4x+4 are x=(3(6+sqrt(6)))/(10),x=(3(6-sqrt(6)))/(10)
Find the zeros of (9-x^2)/9 =x^2-4x+4
The zeros of (9-x^2)/9 =x^2-4x+4 are x=(3(6+sqrt(6)))/(10),x=(3(6-sqrt(6)))/(10)