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

The answer to sqrt(x^2+1)-1/2 =x is x= 3/4

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sqrt(x^2+1)-1/2 =x

x^{2} + 1 - \frac{1}{2} = x

x = \frac{3}{4}

Decimal Notation

x = 0.75

Solution steps

x^{2} + 1 - \frac{1}{2} = x

Multiply both sides by

2

x^{2} + 1 \cdot 2 - \frac{1}{2} \cdot 2 = x \cdot 2

Simplify

2 x^{2} + 1 - 1 = x \cdot 2

Remove square roots

4 x^{2} + 4 = 4 x^{2} + 4 x + 1

Solve

4 x^{2} + 4 = 4 x^{2} + 4 x + 1 : x = \frac{3}{4}

x = \frac{3}{4}

Verify Solutions:

x = \frac{3}{4}

True

The solution is

x = \frac{3}{4}

x + 1 - 4 x - 3 = 1

7 x^{\frac{5}{4}} - 14 = 0

\frac{1}{1 - x ^{2}} = 2

2 k + 24 = - 8 - 2 k

x^{2} - 5 x = x - 4

What is the answer to sqrt(x^2+1)-1/2 =x ?
The answer to sqrt(x^2+1)-1/2 =x is x= 3/4
Solve for x: sqrt(x^2+1)-1/2 =x
The solution is x= 3/4