Solve 2sqrt{2-7x}=sqrt{-36x}

$$2 \sqrt{ 2-7x } = \sqrt{ -36x }$$

Solve for x

$$x=-1$$

Solution Steps

Square both sides of the equation.

$$\left(2\sqrt{2-7x}\right)^{2}=\left(\sqrt{-36x}\right)^{2}$$

Expand \left(2\sqrt{2-7x}\right)^{2}.

$$2^{2}\left(\sqrt{2-7x}\right)^{2}=\left(\sqrt{-36x}\right)^{2}$$

Calculate 2 to the power of 2 and get 4.

$$4\left(\sqrt{2-7x}\right)^{2}=\left(\sqrt{-36x}\right)^{2}$$

Calculate \sqrt{2-7x} to the power of 2 and get 2-7x.

$$4\left(2-7x\right)=\left(\sqrt{-36x}\right)^{2}$$

Use the distributive property to multiply 4 by 2-7x.

$$8-28x=\left(\sqrt{-36x}\right)^{2}$$

Calculate \sqrt{-36x} to the power of 2 and get -36x.

$$8-28x=-36x$$

Add 36x to both sides.

$$8-28x+36x=0$$

Combine -28x and 36x to get 8x.

$$8+8x=0$$

Subtract 8 from both sides. Anything subtracted from zero gives its negation.

$$8x=-8$$

Divide both sides by 8.

$$x=\frac{-8}{8}$$

Divide -8 by 8 to get -1.

$$x=-1$$

Substitute -1 for x in the equation 2\sqrt{2-7x}=\sqrt{-36x}.

$$2\sqrt{2-7\left(-1\right)}=\sqrt{-36\left(-1\right)}$$

Simplify. The value x=-1 satisfies the equation.

$$6=6$$

Equation 2\sqrt{2-7x}=\sqrt{-36x} has a unique solution.

$$x=-1$$