Solve sqrt{2x+5}=sqrt{4x+9}

$$\sqrt{ 2x+5 } = \sqrt{ 4x+9 }$$

Solve for x

$$x=-2$$

Solution Steps

Square both sides of the equation.

$$\left(\sqrt{2x+5}\right)^{2}=\left(\sqrt{4x+9}\right)^{2}$$

Calculate \sqrt{2x+5} to the power of 2 and get 2x+5.

$$2x+5=\left(\sqrt{4x+9}\right)^{2}$$

Calculate \sqrt{4x+9} to the power of 2 and get 4x+9.

$$2x+5=4x+9$$

Subtract 4x from both sides.

$$2x+5-4x=9$$

Combine 2x and -4x to get -2x.

$$-2x+5=9$$

Subtract 5 from both sides.

$$-2x=9-5$$

Subtract 5 from 9 to get 4.

$$-2x=4$$

Divide both sides by -2.

$$x=\frac{4}{-2}$$

Divide 4 by -2 to get -2.

$$x=-2$$

Substitute -2 for x in the equation \sqrt{2x+5}=\sqrt{4x+9}.

$$\sqrt{2\left(-2\right)+5}=\sqrt{4\left(-2\right)+9}$$

Simplify. The value x=-2 satisfies the equation.

$$1=1$$

Equation \sqrt{2x+5}=\sqrt{4x+9} has a unique solution.

$$x=-2$$