Solve x=sqrt{8x+20}

$$x= \sqrt{ 8x+20 }$$

Solve for x

$$x=10$$

Solution Steps

Square both sides of the equation.

$$x^{2}=\left(\sqrt{8x+20}\right)^{2}$$

Calculate \sqrt{8x+20} to the power of 2 and get 8x+20.

$$x^{2}=8x+20$$

Subtract 8x from both sides.

$$x^{2}-8x=20$$

Subtract 20 from both sides.

$$x^{2}-8x-20=0$$

To solve the equation, factor x^{2}-8x-20 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.

$$a+b=-8 ab=-20$$

Since ab is negative, a and b have the opposite signs. Since a+b is negative, the negative number has greater absolute value than the positive. List all such integer pairs that give product -20.

$$1,-20 2,-10 4,-5$$

Calculate the sum for each pair.

$$1-20=-19 2-10=-8 4-5=-1$$

The solution is the pair that gives sum -8.

$$a=-10 b=2$$

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

$$\left(x-10\right)\left(x+2\right)$$

To find equation solutions, solve x-10=0 and x+2=0.

$$x=10 x=-2$$

Substitute 10 for x in the equation x=\sqrt{8x+20}.

$$10=\sqrt{8\times 10+20}$$

Simplify. The value x=10 satisfies the equation.

$$10=10$$

Substitute -2 for x in the equation x=\sqrt{8x+20}.

$$-2=\sqrt{8\left(-2\right)+20}$$

Simplify. The value x=-2 does not satisfy the equation because the left and the right hand side have opposite signs.

$$-2=2$$

Equation x=\sqrt{8x+20} has a unique solution.

$$x=10$$