What is the answer to xsqrt(c^2x^2-1)=cx^2-x ?

The answer to xsqrt(c^2x^2-1)=cx^2-x is x=0 {No Solution},x= 1/c {c 0}

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xsqrt(c^2x^2-1)=cx^2-x

x c^{2} x^{2} - 1 = c x^{2} - x

x = 0 {No Solution}, x = \frac{1}{c} {c < 0 or c > 0}

Solution steps

x c^{2} x^{2} - 1 = c x^{2} - x

Subtract

c x^{2} - x

from both sides

x c^{2} x^{2} - 1 - (c x^{2} - x) = c x^{2} - x - (c x^{2} - x)

Simplify

c^{2} x^{2} - 1 x - c x^{2} + x = 0

Factor

c^{2} x^{2} - 1 x - c x^{2} + x : x (c^{2} x^{2} - 1 - c x + 1)

x (c^{2} x^{2} - 1 - c x + 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or c^{2} x^{2} - 1 - c x + 1 = 0

Solve

c^{2} x^{2} - 1 - c x + 1 = 0 : x = \frac{1}{c} {c < 0 or c > 0}

x = 0, x = \frac{1}{c} {c < 0 or c > 0}

Verify Solutions:

x = 0 {No Solution}, x = \frac{1}{c} {c < 0 or c > 0}

The solutions are

x = 0 {No Solution}, x = \frac{1}{c} {c < 0 or c > 0}

x - 6 x - 27 = 0

5 - 2 x - 3 = 0

x, 3 x + x = 0

What is the answer to xsqrt(c^2x^2-1)=cx^2-x ?
The answer to xsqrt(c^2x^2-1)=cx^2-x is x=0 {No Solution},x= 1/c {c<0\lor c>0}