What is the answer to (2x-5)^2+(3x-3)^2=13x^2-5x+7 ?

The answer to (2x-5)^2+(3x-3)^2=13x^2-5x+7 is x= 9/11

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(2x-5)^2+(3x-3)^2=13x^2-5x+7

(2 x - 5)^{2} + (3 x - 3)^{2} = 13 x^{2} - 5 x + 7

x = \frac{9}{11}

Decimal Notation

x = 0.81818 \dots

Solution steps

(2 x - 5)^{2} + (3 x - 3)^{2} = 13 x^{2} - 5 x + 7

Expand

(2 x - 5)^{2} + (3 x - 3)^{2} : 13 x^{2} - 38 x + 34

13 x^{2} - 38 x + 34 = 13 x^{2} - 5 x + 7

Move

34

to the right side

13 x^{2} - 38 x = 13 x^{2} - 5 x - 27

Subtract

13 x^{2} - 5 x

from both sides

13 x^{2} - 38 x - (13 x^{2} - 5 x) = 13 x^{2} - 5 x - 27 - (13 x^{2} - 5 x)

Simplify

- 33 x = - 27

Divide both sides by

- 33

x = \frac{9}{11}

2 (1 + x) - 3 (x - 1) - 6 = x - 11

2 + 3 = 5

4 x + 20 = 45 - x

7.3 - \frac{3 ( x + 2 )}{2} = \frac{2 x}{3} - \frac{x + 7}{2}

\frac{2}{3} (9 x - 15) = 2 (3 x - 5)

What is the answer to (2x-5)^2+(3x-3)^2=13x^2-5x+7 ?
The answer to (2x-5)^2+(3x-3)^2=13x^2-5x+7 is x= 9/11
Solve for x: (2x-5)^2+(3x-3)^2=13x^2-5x+7
The solution is x= 9/11