Solve x=sqrt{11x-30}

$$x = \sqrt { 11 x - 30 }$$

Solve for x

$$x=6$$

$$x=5$$

Solution Steps

Square both sides of the equation.

$$x^{2}=\left(\sqrt{11x-30}\right)^{2}$$

Calculate \sqrt{11x-30} to the power of 2 and get 11x-30.

$$x^{2}=11x-30$$

Subtract 11x from both sides.

$$x^{2}-11x=-30$$

Add 30 to both sides.

$$x^{2}-11x+30=0$$

To solve the equation, factor x^{2}-11x+30 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.

$$a+b=-11 ab=30$$

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 30.

$$-1,-30 -2,-15 -3,-10 -5,-6$$

Calculate the sum for each pair.

$$-1-30=-31 -2-15=-17 -3-10=-13 -5-6=-11$$

The solution is the pair that gives sum -11.

$$a=-6 b=-5$$

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

$$\left(x-6\right)\left(x-5\right)$$

To find equation solutions, solve x-6=0 and x-5=0.

$$x=6 x=5$$

Substitute 6 for x in the equation x=\sqrt{11x-30}.

$$6=\sqrt{11\times 6-30}$$

Simplify. The value x=6 satisfies the equation.

$$6=6$$

Substitute 5 for x in the equation x=\sqrt{11x-30}.

$$5=\sqrt{11\times 5-30}$$

Simplify. The value x=5 satisfies the equation.

$$5=5$$

List all solutions of x=\sqrt{11x-30}.

$$x=6 x=5$$