What is the answer to sqrt(2w)+sqrt(8w)=4w+1 ?

The answer to sqrt(2w)+sqrt(8w)=4w+1 is w= 1/2 ,w= 1/8

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sqrt(2w)+sqrt(8w)=4w+1

2 w + 8 w = 4 w + 1

w = \frac{1}{2}, w = \frac{1}{8}

Decimal Notation

w = 0.5, w = 0.125

Solution steps

2 w + 8 w = 4 w + 1

Factor

2 w + 8 w : 32 w

32 w = 4 w + 1

Square both sides:

18 w = 16 w^{2} + 8 w + 1

18 w = 16 w^{2} + 8 w + 1

Solve

18 w = 16 w^{2} + 8 w + 1 : w = \frac{1}{2}, w = \frac{1}{8}

w = \frac{1}{2}, w = \frac{1}{8}

Verify Solutions:

w = \frac{1}{2}

True

, w = \frac{1}{8}

True

The solutions are

w = \frac{1}{2}, w = \frac{1}{8}

x = 1 - x^{2}

3 y - 1 = 2 8 - 2 y

2 x + 3 + x + 2 = 2

32 + 4 x = x

8 x - 16 = 0

What is the answer to sqrt(2w)+sqrt(8w)=4w+1 ?
The answer to sqrt(2w)+sqrt(8w)=4w+1 is w= 1/2 ,w= 1/8
Solve for w: sqrt(2w)+sqrt(8w)=4w+1
The solution is w= 1/2 ,w= 1/8