Solve x=sqrt{6x-8}

$$x= \sqrt{ 6x-8 }$$

Solve for x

$$x=4$$

$$x=2$$

Solution Steps

Square both sides of the equation.

$$x^{2}=\left(\sqrt{6x-8}\right)^{2}$$

Calculate \sqrt{6x-8} to the power of 2 and get 6x-8.

$$x^{2}=6x-8$$

Subtract 6x from both sides.

$$x^{2}-6x=-8$$

Add 8 to both sides.

$$x^{2}-6x+8=0$$

To solve the equation, factor x^{2}-6x+8 using formula x^{2}+\left(a+b\right)x+ab=\left(x+a\right)\left(x+b\right). To find a and b, set up a system to be solved.

$$a+b=-6 ab=8$$

Since ab is positive, a and b have the same sign. Since a+b is negative, a and b are both negative. List all such integer pairs that give product 8.

$$-1,-8 -2,-4$$

Calculate the sum for each pair.

$$-1-8=-9 -2-4=-6$$

The solution is the pair that gives sum -6.

$$a=-4 b=-2$$

Rewrite factored expression \left(x+a\right)\left(x+b\right) using the obtained values.

$$\left(x-4\right)\left(x-2\right)$$

To find equation solutions, solve x-4=0 and x-2=0.

$$x=4 x=2$$

Substitute 4 for x in the equation x=\sqrt{6x-8}.

$$4=\sqrt{6\times 4-8}$$

Simplify. The value x=4 satisfies the equation.

$$4=4$$

Substitute 2 for x in the equation x=\sqrt{6x-8}.

$$2=\sqrt{6\times 2-8}$$

Simplify. The value x=2 satisfies the equation.

$$2=2$$

List all solutions of x=\sqrt{6x-8}.

$$x=4 x=2$$