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

The answer to (sqrt(ax+b)-2)/x =1 is x=(-4+a+sqrt(a^2-8a+4b))/2 ,x=(-4+a-sqrt(a^2-8a+4b))/2

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(sqrt(ax+b)-2)/x =1

\frac{a x + b - 2}{x} = 1

x = \frac{- 4 + a + a ^{2} - 8 a + 4 b}{2}, x = \frac{- 4 + a - a ^{2} - 8 a + 4 b}{2}

Solution steps

\frac{a x + b - 2}{x} = 1

Multiply both sides by

x

\frac{a x + b - 2}{x} x = 1 \cdot x

Simplify

a x + b - 2 = x

Remove square roots

a x + b = x^{2} + 4 x + 4

Solve

a x + b = x^{2} + 4 x + 4 : x = \frac{- 4 + a + a ^{2} - 8 a + 4 b}{2}, x = \frac{- 4 + a - a ^{2} - 8 a + 4 b}{2}

x = \frac{- 4 + a + a ^{2} - 8 a + 4 b}{2}, x = \frac{- 4 + a - a ^{2} - 8 a + 4 b}{2}

w = 3

(8 x + 9)^{\frac{3}{2}} + 5 = 130

x + 2 - 1 = x - 3

5 x + 4 = 7

What is the answer to (sqrt(ax+b)-2)/x =1 ?
The answer to (sqrt(ax+b)-2)/x =1 is x=(-4+a+sqrt(a^2-8a+4b))/2 ,x=(-4+a-sqrt(a^2-8a+4b))/2