What is the answer to (x-4)*a=sqrt(x+5)-3 ?

The answer to (x-4)*a=sqrt(x+5)-3 is x=4,x=(4a^2-6a+1)/(a^2) {0<a< 1/3 }

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(x-4)*a=sqrt(x+5)-3

(x - 4) \cdot a = x + 5 - 3

x = 4, x = \frac{4 a ^{2} - 6 a + 1}{a ^{2}} {0 < a < \frac{1}{3}}

Solution steps

(x - 4) a = x + 5 - 3

Expand

(x - 4) a : a x - 4 a

a x - 4 a = x + 5 - 3

Remove square roots

a^{2} x^{2} - 8 a^{2} x + 6 a x + 16 a^{2} - 24 a + 9 = x + 5

Solve

a^{2} x^{2} - 8 a^{2} x + 6 a x + 16 a^{2} - 24 a + 9 = x + 5 : x = 4, x = \frac{4 a ^{2} - 6 a + 1}{a ^{2}}

x = 4, x = \frac{4 a ^{2} - 6 a + 1}{a ^{2}}

Verify Solutions:

x = 4

True

, x = \frac{4 a ^{2} - 6 a + 1}{a ^{2}} {0 < a < \frac{1}{3}}

The solutions are

x = 4, x = \frac{4 a ^{2} - 6 a + 1}{a ^{2}} {0 < a < \frac{1}{3}}

x - 2 = x - 1

x - 2 = x - 2

2 \cdot x - 1 = - 7

x + 2 - 10 = - 6

17 - 4 x = x - 3

What is the answer to (x-4)*a=sqrt(x+5)-3 ?
The answer to (x-4)*a=sqrt(x+5)-3 is x=4,x=(4a^2-6a+1)/(a^2) {0<a< 1/3 }