What is the answer to (2x-3)^2=1+(8x^2+x)/2 ?

The answer to (2x-3)^2=1+(8x^2+x)/2 is x= 16/25

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(2x-3)^2=1+(8x^2+x)/2

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

x = \frac{16}{25}

Solution steps

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

Multiply both sides by

2

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

Expand

2 (2 x - 3)^{2} : 8 x^{2} - 24 x + 18

8 x^{2} - 24 x + 18 = 2 + 8 x^{2} + x

Move

18

to the right side

8 x^{2} - 24 x = 8 x^{2} + x - 16

Subtract

8 x^{2} + x

from both sides

8 x^{2} - 24 x - (8 x^{2} + x) = 8 x^{2} + x - 16 - (8 x^{2} + x)

Simplify

- 25 x = - 16

Divide both sides by

- 25

x = \frac{16}{25}

2 x + 6 = 12

3 x - 15 = 0

\frac{4}{3} y = 16

x, 5 x + 2 y = 16

4 y + 9 - y - 2 y = 16 y + 42

What is the answer to (2x-3)^2=1+(8x^2+x)/2 ?
The answer to (2x-3)^2=1+(8x^2+x)/2 is x= 16/25
Solve for x: (2x-3)^2=1+(8x^2+x)/2
The solution is x= 16/25