Solve sqrt{7x+2}=sqrt{4x+1}

$$\sqrt { 7 x + 2 } = \sqrt { 4 x + 1 }$$

Solve for x (complex solution)

$$x=-\frac{1}{3}\approx -0.333333333$$

Solution Steps

Square both sides of the equation.

$$\left(\sqrt{7x+2}\right)^{2}=\left(\sqrt{4x+1}\right)^{2}$$

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

$$7x+2=\left(\sqrt{4x+1}\right)^{2}$$

Calculate \sqrt{4x+1} to the power of 2 and get 4x+1.

$$7x+2=4x+1$$

Subtract 4x from both sides.

$$7x+2-4x=1$$

Combine 7x and -4x to get 3x.

$$3x+2=1$$

Subtract 2 from both sides.

$$3x=1-2$$

Subtract 2 from 1 to get -1.

$$3x=-1$$

Divide both sides by 3.

$$x=\frac{-1}{3}$$

Fraction \frac{-1}{3} can be rewritten as -\frac{1}{3} by extracting the negative sign.

$$x=-\frac{1}{3}$$

Substitute -\frac{1}{3} for x in the equation \sqrt{7x+2}=\sqrt{4x+1}.

$$\sqrt{7\left(-\frac{1}{3}\right)+2}=\sqrt{4\left(-\frac{1}{3}\right)+1}$$

Simplify. The value x=-\frac{1}{3} satisfies the equation.

$$\frac{1}{3}i\times 3^{\frac{1}{2}}=\frac{1}{3}i\times 3^{\frac{1}{2}}$$

Equation \sqrt{7x+2}=\sqrt{4x+1} has a unique solution.

$$x=-\frac{1}{3}$$