Solve sqrt{3-3x}=sqrt{4x-10}

$$\sqrt { 3 - 3 x } = \sqrt { 4 x - 10 }$$

Solve for x (complex solution)

$$x = \frac{13}{7} = 1\frac{6}{7} \approx 1.857142857$$

Solution Steps

Square both sides of the equation.

$$\left(\sqrt{3-3x}\right)^{2}=\left(\sqrt{4x-10}\right)^{2}$$

Calculate \sqrt{3-3x} to the power of 2 and get 3-3x.

$$3-3x=\left(\sqrt{4x-10}\right)^{2}$$

Calculate \sqrt{4x-10} to the power of 2 and get 4x-10.

$$3-3x=4x-10$$

Subtract 4x from both sides.

$$3-3x-4x=-10$$

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

$$3-7x=-10$$

Subtract 3 from both sides.

$$-7x=-10-3$$

Subtract 3 from -10 to get -13.

$$-7x=-13$$

Divide both sides by -7.

$$x=\frac{-13}{-7}$$

Fraction \frac{-13}{-7} can be simplified to \frac{13}{7} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{13}{7}$$

Substitute \frac{13}{7} for x in the equation \sqrt{3-3x}=\sqrt{4x-10}.

$$\sqrt{3-3\times \frac{13}{7}}=\sqrt{4\times \frac{13}{7}-10}$$

Simplify. The value x=\frac{13}{7} satisfies the equation.

$$\frac{3}{7}i\times 14^{\frac{1}{2}}=\frac{3}{7}i\times 14^{\frac{1}{2}}$$

Equation \sqrt{3-3x}=\sqrt{4x-10} has a unique solution.

$$x=\frac{13}{7}$$